{"id":60786,"date":"2024-09-30T10:36:51","date_gmt":"2024-09-30T10:36:51","guid":{"rendered":"https:\/\/biomedpharmajournal.org\/?p=60786"},"modified":"2024-10-09T18:39:13","modified_gmt":"2024-10-09T18:39:13","slug":"a-hybrid-approach-for-ct-image-noise-reduction-combining-method-noise-cnn-and-shearlet-transform","status":"publish","type":"post","link":"https:\/\/biomedpharmajournal.org\/staging\/vol17no3\/a-hybrid-approach-for-ct-image-noise-reduction-combining-method-noise-cnn-and-shearlet-transform\/","title":{"rendered":"A Hybrid Approach for CT Image Noise Reduction Combining Method Noise-CNN and Shearlet Transform"},"content":{"rendered":"\n

Introduction<\/strong><\/p>\n\n\n\n

Medical imaging refers to the different imaging techniques used in modern hospitals and clinics for medical diagnosis. X-rays, CT imaging, ultrasound scans, magnetic-resonance imaging (MRI) techniques are used to scan within the body to assess the cause of disease and provide appropriate treatment for medical conditions. In CT imaging , X-ray radiation is directed at the patient\u2019s body from multiple projections to scan bone fractures, organs, fat, and blood vessels. Although repeated scans in patients provide invaluable information for the clinical diagnosis of various diseases, there is a potential risk of  cancer threat1,2<\/sup>. Hence, it is essential to minimize radiation exposure. Lowering radiation exposure improves noise, blur and other minute artifacts in tomographical images3<\/sup>. Low dose CT images exhibit noise due to electrical interference, quantum effects and mathematical computations. An effective denoising technique is required to explicitly reduce the noise and artifacts from distorted CT images 4,5<\/sup>. CT image denoising techniques can be classified as classical CT image denoising, post-processing, and deep learning related methods. <\/p>\n\n\n\n

Classical\ndenoising techniques are classified as spatial and transform domain filtering\nmethods. Spatial filtering methods manipulate the intensity values of the pixels\ndirectly based on spatial coordinates. Here, denoising is applied to the whole\nimage. Spatial domain filtering methods,6,7,8,9<\/sup> make use of low-pass\nfiltering, suppressing noise to some extent and resulting in blurry images, for\nexample, wiener, mean, bilateral and nonlocal means (NLM) filtering show the\ncorrelation between pixel intensities in their neighboring pixels around a\ngiven pixel. This results in average smoothing, and a loss of sharp features in\nan image. <\/p>\n\n\n\n

Transform\ndomain filtering methods analyze images in terms of their frequency levels, for\nexample., Discrete fourier transform, Discrete cosine transform, Wavelet, and Shearlet\ntransform domain10,11,12,13<\/sup>. In transform domain filtering, thresholding\nmethod is applied to denoise noisy CT images, and inverse transformation is\nused to reconstruct original images. Thresholding methods like SureShrink, VisuShrink,\nand BayesShrink. VisuShrink is a global thresholding method based on the pixel\nquantity in an image, where as SureShrink and BayesShrink based on each subband\nto evaluate the threshold values. The non-subsampled shearlet transform\nprovides spatial localization and sparse representation of multiscale and\nmultidirectional features to capture different directional features of an image\nto overcome the limitations such as isotropic features and the absence of\nmultidirectionality of the wavelet transform. The shearlet transform is\neffectively used to capture and represent anisotropic features such as edges,\ncorners, and fine details, and well-localized structures exhibit different\nfeatures in different directions.<\/p>\n\n\n\n

Unlike previous denoising\ntechniques, post processing methods explicitly handle the reconstructed images\nin CT imaging, that is reconstruction without projectional data, which improves\nthe performance of generalization. Traditional post-processing methods, Block-matching\nand 3D filtering (BM3D)14<\/sup>, adaptive nonlocal means (NLM)15<\/sup>,\nK means singular-valued decomposition (KSVD)16<\/sup> methods effectively\nreduce noise and artifacts but the computational cost is high.<\/p>\n\n\n\n

Hybrid\nmethods are combinations of spatial and transform domain methods that provide\nimproved image-denoising results, for example, denoising CT images through total\nvariation using the shearlet domain17<\/sup> with a multi-variate model,\nand method noise-based approach yield better results in suppressing noise, preserving\nthe edges and structural details. The detection of noisy COVID-19 (SARS-CoV-2)\nvirus on LDCT imaging using the nonlocal means filter in conjunction with method\nnoise yields improved SSIM results compared to other existing methods18<\/sup>,\nfor example, nonlocal means19<\/sup> , total-variation methods20<\/sup>\nusing wavelets, to reduce noise while preserving image features in detail. However,\nimages suffer from noise and artifacts owing to poor directionality, shift\nsensitivity, and a limited ability to capture directional information.<\/p>\n\n\n\n

Recently, deep learning  techniques have played a crucial role in image denoising.The progress in CNN-based methods21,22<\/sup>  has improved in CT image denoising in LDCT imaging. The deep denoising convolutional neural network with residual learning strategy (REDCNN) is a CNN architecture used in image denoising that includes residual mapping trained deeper networks to resolve the vanishing-gradient problem and allows deeper networks to be trained easily. The efficiency of the deep CNN differs at different CT radiation dose levels. For example, the Wasserstein distance-based generative adversarial network (W-GAN) provides superior GAN performance, and perceptual loss evaluates perceptual features with filtered output at ground truth level to maintain critical information and effectively reduce noise in CT images23<\/sup>. Currently, transformer models play a significant role in image- processing. The Transformer model is a (DL) deep learning architecture, which is a self-attention mechanism that captures long-range dependencies between input and output tokens24<\/sup>. A vision transformer (ViT) is a kind of neural-network framework, especially applied in domains like image recognition, recognition, and segmentation. Transformer-based Encoder-decoder Dilation network (TED) effectively preserves the structure and fine details while denoising images25<\/sup>.<\/p>\n\n\n\n

Problem Statement<\/strong><\/p>\n\n\n\n

CT imaging is essential for accurate healthcare diagnostics because it provides precise images for the detection of  health conditions. However, the existence of Gaussian noise in CT images significantly diminishes their quality, contributing to potential challenges in disease prediction and identification. This study aims to address the significant need for effective noise suppression method to improve CT image quality, thereby improving diagnostic precision and patient clinical judgement.<\/p>\n\n\n\n

Major Contribution<\/strong><\/p>\n\n\n\n

The study presents a novel CT imaging denoising technique that combines method noise-based CNN with a non-subsampled shearlet transform to effectively mitigate Gaussian noise .The proposed technique improves noise suppression while retaining crucial image features by leveraging the multi-scale and multi-directional analysis of the shearlet transform. Additionally, the method noise-based CNN method intends to reduce residual noise patterns in denoised CT images. This hybrid strategy significantly improves image quality and diagnostic accuracy, providing an effective solution to noise-related challenges in LDCT imaging.<\/p>\n\n\n\n

The rest of this paper is presented as follows. Section 2 introduces a brief literature review of CT image-denoising approaches. Section 3 outlines the major concepts of shearlet transform and DnCNN architecture. Section 4 discusses the proposed hybrid algorithm for CT image denoising with a method noise-based CNN method using a shearlet transform. The findings from the experiments and a comparison with various existing denoising methods are shown in Section 5. Finally, the conclusions and proposed future studies are presented in Section 6.<\/p>\n\n\n\n

Literature Review<\/strong><\/p>\n\n\n\n

Clinical imaging plays a major role\nin diagnostic decision making using different modalities, to improve the\naccuracy of clinical diagnosis of the internal human body. In,26 <\/sup> Abhisheka proposed that the prominent medical\nimaging modalities include X-radiation, CT scan, MRI, Positron-Emission Tomographical\n(PET) imaging, and Ultrasound scans. These modalities effectively visualize a\ndetailed image of inside the human body. For example, X-rays can be used to\nidentify bone fractures, dislocations. Unlike X-ray, a CT scan provides a fast,\nmore detailed image for medical diagnosis. CT scan is used to detect organ\nabnormalities, blood clots, subtle bone fractures, and internal bleeding. MRI\nscans provide highly detailed images of soft tissues. Ultrasound, or\nsonography, exploits  high frequency  sound waves to provide detailed imaging of\nhuman body, detect problems in the liver, kidney, heart, blood vessels,\nvalvular regurgitation, and abdominal aorta etc. PET scans are used for\ndetecting organ abnormalities, including soft tissue-related issues such as finding\ntumors, neurological (brain) diseases, cardiovascular (heart) diseases. These medical\nimage modalities are used by healthcare professionals to diagnose various\nmedical conditions in a timely, accurate, and non-invasive manner, thereby\nimproving patient outcomes.<\/p>\n\n\n\n

The\nproposed literature review primarily concentrates on CT imaging using various\ndeep learning approaches. In,27<\/sup> Sehgal proposed\nnovel CT image denoising algorithm, Political-Taylor Anti-coronavirus\nOptimization (PT-ACVO) combines deep learning and advanced optimization\ntechniques to mitigate noise and enhance image qualities effectively. The\nmethod detects noisy pixels in images using a Deep Residual  network (DRN) and reconstructs them using the\nPolitical Taylor-Anti-Coronavirus Optimization (Political Taylor -ACVO)\nalgorithm and image-enhancement is achieved through Vectorial-Total-Variation\napproach. Image denoising was performed using Discrete Wavelet transform and\nNLM filtering, followed by image fusion to obtain final denoised image.\nHowever, the DRN and the Political-Taylor-ACVO Optimization algorithm might\ncause higher computational complexity and there is a requirement for extensive\nparameter-tuning.<\/p>\n\n\n\n

The evolution of Deep\nlearning methods has emerged as a rapid progress in CT image denoising28<\/sup>.\nTo improve the quality of LDCT imaging,29<\/sup> Zhang proposed an innovative\ndenoising method using U-net and multi-attention mechanisms for effective\nfeature extraction. This includes three attention modules. The local attention\nmodule provides localized surrounding pixel feature extraction based on feature\nmapping. The multi feature and channel-attention-module automatically acquire, extract,\nsuppress noise, and contribute different weights to the existing feature-map based\non different tasks. The hierarchical identification module enabled a deeper CNN\nfor a substantial amount of feature extraction. Additionally, a study suggests\nthat the enhanced learning-module increases the network depth by stacking a\nmulti-layered CNN, activation layer and batch-normalization (BN) enabling the\nlearning and maintenance of  detailed\nimage information. The Experimental quantitative analysis results show that the\nmodule effectively suppressed noise.<\/p>\n\n\n\n

In,30<\/sup> Huang proposed a\ndeep cascade residual network (DCRN) that offers promising denoising results,\ncombining attention mechanisms to enhance model performance, a hybrid loss\nfunction to provide better generalization ability of the model, and iterative\nrefinement to iteratively refine the denoised image to obtain a better-quality\nimage. In,31<\/sup> Selig proposed a Dilated Residual U-Net (DRU-Net) for\nbetter LDCT image reconstruction and image enhancement to enhance image quality\nand performance. This involves two-stage process: Initially, filtered-back\nprojection (FBP) was performed to improve image reconstruction. DRU-Net is\npre-trained for denoising natural grayscale images, and mapping low-dose filtered\nback projection is applied to the reconstructed images to enhance the CT\nimages. DRU-Net is fine-tuned and performs downstream image enhancement  by leveraging LDCT imaging  and appropriate normal-dose computed tomographical\n(NDCT) images. This method secured the topmost ranking in the low dose parallel\nbeam CT-challenge (LoDoPaB), was computationally more efficient than Institute\nof Technology Network (ItNet), and increased the SSIM metric value. Here, the\nU-Net model was pretrained only for Gaussian denoising. If the pre-trained task\nand target CT image denoising differ, affects the performance of the model.<\/p>\n\n\n\n

In,32<\/sup> Song introduced a NeXtResUNet-CNN\nfor industrial CT image denoising. It includes industrial CT image systems that\noperate on diverse energies and significantly affect distinct spatial\nresolutions. The proposed algorithm initiates an image fusion network that\ncombines Con-vNeXt, ResNet, and U-Net, is assigned to a self-generated industrial\ntomographic denoising dataset. NeXtResUnet simulates a transformer model to\nacquire global features, and ResNet is used to extract the image details. CT-image\nnoise reduction can be accomplished by downsampling the CNN. This results in an\nimproved Peak signal-to-noise ratio (PSNR) and image-denoising, image\nsegmentation, and contrast normalization. The NeXtResUNet network structure is\nconcise and expandable, making it applicable to image denoising and image vision-based\ntasks, like CT image super-resolution and auto-segmentation involving\nindustrial CT data. <\/p>\n\n\n\n

In,33<\/sup> Byeon proposed the\nuse of a lightweight Deep CNN with multi-directional fuzzy non subsampled shearlet\ntransformation (FNSST) for better image decomposition and suppression of noisy patterns\nand artifacts in LDCT imaging. FNSST is a multi-scale and multi-directional\nlocalization technique used for the decomposition of low and normal dose images\nto produce high and low-resolutional subimages. High-resolutional subimages\nwith varying noise levels in a fuzzy setting and other artifacts were given as\ninput to the CNN to establish an association between the LDCT high-resolution subimages\nand  the residual subimages generated\nthroughout the training process. FNSST-CNN discriminates low and high-frequency\nsubimages while testing process to suppress noise and other relevant artifacts.\nIn LDCT imaging, FNSST-CNN effectively reduces noisy patterns while preserving the\nedges and structural features. The main limitation is that the cost of\nimplementing fuzzy-based methods is high.<\/p>\n\n\n\n

In,34<\/sup> Li proposed a\nmultistage noise reduction framework for LDCT images. The framework was mainly trained\nusing un-paired data. The (PCCNN) Progressive-Cyclical-CNN  performs latent -space utilization from CT\nimages to suppress noisy areas and other artifacts. PCCNN, a multistage\ndenoising framework, suggests a noise transfer model that enables the transfer\nof noise from low-dose to normal dose CT images. The PCCNN also has a\nprogressive module that includes a multi-stage wavelet transform to extract\nhigh frequency coefficients to reduce noisy coefficients and preserve contours\nof the image. The main constraint is that there is a need for pairs of\nperfectly matched low and normal-dose images to elevate model performance. <\/p>\n\n\n\n

In,35 <\/sup>\u00c7ali\u015fkan introduced, effective method for identifying and handling noisy pixels in 2D images using  to enhance the quality of CT images, specifically focusing on accurate detection of noisy pixels in  2 Dimensional CT images using hidden resource decomposition approach. The hidden resource decomposition approach with extreme learning Machines (ELM) to improve efficiency in training and high learning speed suitable for handling large volumes of the CT images to preserve critical structural information in detail. The ELM method markedly improved noise suppression and imaging quality, attaining peak performance with 250 hidden layer neurons. he ELM method significantly reduced mean- squared-error (MSE) and peak-signal-to-noise ratio (PSNR).The incorporation of hidden resource decomposition with ELM may result in complexity in implementation.In,36<\/sup> \u00c7ali\u015fkan suggested, deep learning-driven hybrid approach to categorize seven mineral types, with precision, employing refined feature selection and the complement rule for clustering. The method utilizes deep learning models for feature-extraction and applied metaheuristic optimization to identify key features, and complement rule for grouping ineffective features for achieving exceptional classification precision. The image denoising can be obtained using metaheuristic optimization algorithm due to their capability to explore vast and complex search spaces.<\/p>\n\n\n\n

Major Concepts<\/strong><\/p>\n\n\n\n

The following section presents some\nessential concepts that were exploited to implement the proposed methodology.<\/p>\n\n\n\n

Non-subsampled Shearlet Transform <\/strong><\/p>\n\n\n\n

The NSST transform is constitutes\nan extended variant form of wavelet transformation and is a mathematical tool,37<\/sup>\nused in image processing, particularly for image denoising and feature\nextraction. The nonsubsampled shearlet transform is a  multi-directional, multi-dimensional,\nshift-invariant, and well-localized analysis that combines multiscale and\ndirectional analysis separately. NSST coefficients are related to sparse and\ncapture the mathematical and geometric properties of an image. NSST is depicted\nin conjunction with Nonsubsampled-Laplacian pyramid (NS-LP) and shearing-filters.\nInitially, (NSLP) is used to analyze the images into different low\n(approximation) and high (detail) frequency components, and directional\nfiltering helps to generate various subbands and extract shearlet components.\nThe shear matrix accomplishes directional filtering and provides an analysis\nacross various directions.<\/p>\n\n\n\n

For image data with dimensions of n=2, and for j>0, k \u2208 R, l<\/em> \u2208 R2 <\/sup><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Where \u03c8f(j, k, l)<\/em> are called shearlets. Here, j <\/em>> 0, k<\/em> \u2208 R, l<\/em> \u2208 R2<\/sup><\/em>, the shearlets are evaluated as:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The anisotropic-dilation is represented as:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

where j>0, manages the shearlet\u2019s scale, and provides the frequency to obtain finer scales. The shearing transformation matrix is obtained as follows: <\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The\nshearing matrix manages only the shearlet direction.<\/p>\n\n\n\n

Hence,\nthe shearlet transform is determined by the three variables, includes scale j,\norientation k and location l.<\/p>\n\n\n\n

Each f<\/em> \u2208 L2<\/sup> <\/em>(R<\/em>2<\/sup>)is restored using:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Discrete shearlet transform is used to represent multi-dimensional functions. Here j<\/em>= 2-2m<\/sup> ,k=-L<\/em> with m, l=k<\/em>\u2208Z<\/i>2<\/i><\/sup> and L<\/em> \u2208 Z.<\/em><\/p>\n\n\n\n

The Discrete shearlet transformation can be denoted as:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

From each function f<\/em> \u2208 L2<\/sup> <\/em>(R2<\/sup><\/em>),the given method is reconstructed using the characteristics of as described below:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The fundamental framework of DnCNN is depicted in Fig. 1.<\/strong><\/p>\n\n\n\n\n\n
\"\"<\/td>\n\n

Figure 1: <\/strong>Framework of the DnCNN network<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n

Architecture\nof DnCNN<\/strong><\/p>\n\n\n\n

The DnCNN architecture,28<\/sup> has been extensively utilized in image restoration and artifact removal. DnCNN is a popular neural network denoising framework that is intended to denoise additive white Gaussian noise, image restoration, single image super-resolution, and deblocking JPEG images. For a given noisy input image, the noise observation is denoted as x = y + v, and the discriminative model for denoising attempts to acquire the mapping-function, F(x) = y. The DnCNN approach leverages the residuals or skip connection learning process to train the residual transformation R(x) =<\/strong> v; subsequently, y = x – R(x), and DnCNN applies the loss function (l<\/em>) to enhance model parameters that are R (\u2202) specific to the DnCNN framework.<\/p>\n\n\n\n

The Loss function\nis calculated as the average mean-squared error among the residual and the predicted\nimage based on noisy images.<\/p>\n\n\n\n

The training process of the DnCNN was performed using a loss function.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

where,<\/p>\n\n\n\n

\u2202 represents trainable parameters of the DnCNN network.<\/p>\n\n\n\n

N\nrepresents the pairs of clean and distorted training image patches.<\/p>\n\n\n\n

The\narchitecture of the DnCNN was accustomed to reduce boundary artifacts. It\nincludes<\/p>\n\n\n\n

Deep Architecture<\/strong><\/p>\n\n\n\n

DnCNN architecture with depth D, includes 3 types of layers.<\/p>\n\n\n\n

Layer 1<\/strong><\/p>\n\n\n\n

Convolutional_layers + ReLu (Rectified Linear Unit) activation function, including 64 filters with each aspect of existed dimensions [3 \u00d7 3 \u00d7 c] (total channels) to generate 64 feature representations and Rectified Liner Units. Here, non linearity is obtained by ReLu ((max (0,.)). Here, the channel quantity for grayscale image is 1; The number-of-channels for a color image is 3 (R-red, G-green, B-blue). <\/p>\n\n\n\n

Layer 2<\/strong><\/p>\n\n\n\n

Convolutional_layer +<\/strong> ReLu + <\/strong>Batch normalization (BN) through the addition of 64 convolutional_filters, the size of each dimension is  3 \u00d7 3 \u00d7 64, batch normalization was performed  between each aspect of the convolutional_layer and the (ReLu ) activation function, and the depth of the layers was 2 ~ (D – 1).<\/p>\n\n\n\n

Layer 3<\/strong><\/p>\n\n\n\n

The convolutional_layer is mainly applied for image restoration via 64 filters of size 3 \u00d7 3 \u00d7 64.<\/p>\n\n\n\n

Reducing Boundary Artifacts<\/strong><\/p>\n\n\n\n

In general, core vision techniques require the size of resulting image to be consistent with the given input image. Here, DnCNN applies simple-zero padding and  does not exhibit any artifacts. DnCNN directly pads the zeroes before convolution; thus, each feature mapping relating to existing middle layers exhibit a size equivalent to that of the specified image.<\/p>\n\n\n\n

The main\ncontribution of DnCNN in noise reduction approach is that, it effectively\nutilizes the residual network strategy and batch normalization process to\nexpedite the training and regularize the learning problem. The image Denoising approach\nis represented as a Discriminative-learning challenge  to separate distortion from latent images.<\/p>\n\n\n\n

Method\nnoise refers to residual noise or artifacts introduced by the denoising\nalgorithm used in image processing. The residual noise retains pixel\ninformation in the image after applying a noise suppression or denoising\nalgorithm. This shows the\ndiscrepancy among a noisy input and a (filtered) denoised image.<\/p>\n\n\n\n

Method\nnoise = noisy input image – denoised (processed) image.<\/p>\n\n\n\n

Method\nnoise was applied to assess the effectiveness of the denoising techniques while\npreserving image structure and fine details.<\/p>\n\n\n\n

Proposed Methodology<\/strong><\/p>\n\n\n\n

In this\nportion, firstly describe the flowchart and proposed methodology in detail.<\/p>\n\n\n\n

Mathematically, image denoising can\nbe represented as:<\/p>\n\n\n\n

 Y1 (i, j) = X1 (i, j) + n1(i, j).<\/p>\n\n\n\n

where X1 (i, j) denotes a clean\nimage, Y1 (i, j) denotes a noisy or distorted  CT image, and n1 is supposed to be (AWGN) Additive-White-Gaussian-Noise\nin conjunction with a standard deviation (\u03c3), and (i, j) represents pixel\u2019s\nlocations in an image.<\/p>\n\n\n\n

The comprehensive summary of the suggested  approach is depicted in Fig. 2. The proposed hybrid approach combining the preprocessing approach of NSST and postprocessing approach of method noise with CNN to achieve superior denoising results, i.e., effectively combining the structural features of NSST, the statistical features of Bayesian thresholding,38<\/sup> and the learning capability of method noise-based CNN ,39<\/sup> will further enhance the image denoising approach.<\/p>\n\n\n\n\n\n
\"\"<\/td>\n\n

Figure 2:<\/strong> Flowchart of proposed <\/strong>CT image denoising using NSST with method noise-based CNN.<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n

Proposed Algorithm<\/strong><\/p>\n\n\n\n

Input: A Pre-processed, noisy CT image Ai,j<\/sub>.<\/em> <\/p>\n\n\n\n

Output: Final denoised CT image A”i,j<\/sub>.<\/em> <\/p>\n\n\n\n

Step 1: Perform NSST transform to decompose gaussian noisy input CT image Ai,j<\/sub><\/em> to acquire low- frequency components NSSTA<\/sub>l<\/sup> <\/em>and high-frequency components NSSTA<\/sub>l<\/sup><\/em> (HL new<\/sup>, LH new<\/sup> and HH new<\/sup>).<\/p>\n\n\n\n

Step 2: Implement CT image denoising using the following steps:<\/p>\n\n\n\n

Evaluate noise variability.<\/p>\n\n\n\n

Determine thresholding value.<\/p>\n\n\n\n

Implement empirical Bayesian thresholding method on noisy  coefficients to obtain thresholded NSST coefficients.<\/p>\n\n\n\n

Evaluate Noise Variance<\/strong><\/p>\n\n\n\n

Estimate noise variance \u03c3 \u0303noisy<\/em> from noisy shearlet coefficients using robust median estimation 40<\/sup> of CT image noise level in (HH) high-high shearlet diagonal coefficients.<\/p>\n\n\n\n

Estimate the noise standard deviation \u03c3 \u0303noisy<\/em> <\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

med<\/em>= median (|ck<\/sub><\/em> (:)|), \u2208HH<\/em> subbands<\/p>\n\n\n\n

where<\/p>\n\n\n\n

ck<\/sub><\/em> represents set of high frequency (HH) coefficients of NSST decomposition of noisy CT image.<\/p>\n\n\n\n

med<\/em> represents median absolute deviation  of all coefficients.<\/p>\n\n\n\n

The\nconstant 0.6745 is used for robust estimation of the noise level.<\/p>\n\n\n\n

Calculate noise variance \u03c3 \u0303noisy2<\/sup><\/em><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Implement Bayesian Thresholding Process<\/strong><\/p>\n\n\n\n

The threshold value is calculated for retaining\nthe image\u2019s intricate details of an image and perform noise suppression\neffectively.<\/p>\n\n\n\n

The threshold value is selected as:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

where,<\/p>\n\n\n\n

\u2144 \u0303i,j<\/sub><\/em> denotes the threshold value used for empirical Bayes thresholding.<\/p>\n\n\n\n

\u03c3 \u0303noisy2<\/sup><\/em>  <\/sup>denotes the estimated noise variation.<\/p>\n\n\n\n

\u2205n<\/sup> (Ai,j<\/sub>)<\/em> denotes the amount of elements of image Ai,j.<\/p>\n\n\n\n

log\nsignifies the natural logarithm function.<\/p>\n\n\n\n

Perform thresholding of coefficients tk<\/sub><\/em> using empirical Bayes thresholding.<\/p>\n\n\n\n

Bayesian soft thresholding process:<\/p>\n\n\n\n

For each coefficient|Ai,j<\/em>|, <\/strong>find the absolute value of Ai,j. <\/em> <\/p>\n\n\n\n

Compute the sign of the coefficients.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Apply Bayesian soft thresholding approach for each coefficient, is described as: <\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

This function works as follows for\nthresholding:<\/p>\n\n\n\n

 If |Ai,j| is  less than or equal to (<=), the given thresholding A \u0303 i,j<\/em> is set to 0. This procedure effectively removes small coefficients assumed to be dominated by gaussian noise. Then replace the original noisy coefficients Ai,j<\/em> with thresholded coefficients tk<\/sub><\/em> <\/p>\n\n\n\n

Step 3: Perform inverse NSST transform on thresholded NSSTA<\/sub>h<\/sup><\/em>  coefficients (HLnew<\/sup>, LH new<\/sup> and <\/sup>HH new<\/sup>) to reconstruct the semi denoised CT image, Bi,j<\/sub><\/em>.<\/p>\n\n\n\n

Calculate the residual image A\u2019i,j.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Here A’i,j<\/em> represents the discrepancy between a noisy image Ai,j<\/em> and its reconstructed semi denoised image counterpart Bi,j<\/sub><\/em>.<\/p>\n\n\n\n

When A\u2019i,j<\/em> approaches 0, the noise in the original signal is successfully eliminated through denoising. A\u2019i,j<\/em> is residual image that also has some noisy coefficients that affect the quality of image.<\/p>\n\n\n\n

Step 4: Calculate C\u2019i,j<\/em> by applying method noise CNN on residual image A\u2019 <\/em>i.e., DnCNN on (A’i,j).<\/p>\n\n\n\n

Step 5: calculate final denoised image<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

By combining inverse thresholded NSST coefficients (Bi,j)<\/em> with the denoised method noise-based CNN on the residual image (Ci,j)<\/em> to get the final denoised image (A\u2019\u2019i,j)<\/em>.<\/p>\n\n\n\n

A Brief Explanation of Proposed Methodology<\/strong><\/p>\n\n\n\n

During the experiments , noisy CT\nimages are commonly contaminated by Gaussian noise, The hybrid approach, non-subsampled\nshearlet transform is applied for decomposition of noisy image into an\napproximation  (LL new<\/sup>) and detail\npart  (LH new<\/sup>, HL new<\/sup>\nand HH new<\/sup>). The (approximation) high frequency components are further\ndecomposed into multidirectional subbands to represent image features in a\ndetailed manner. The noise variance was estimated in high frequency components using\nthe median-absolute-deviation (MAD).The Bayesian thresholding function, which\nselects all noisy NSST coefficients, then calculates optimal threshold values\nto obtain the denoised coefficients. The inverse NSST transform is used to\nreconstruct denoised CT images from high frequency thresholded NSST\ncoefficients, resulting in a denoised CT image. The denoised image, that is,\nthe reconstructed image, preserves fine details but  retains some residual noise. To solve this\nproblem, calculated the method noise to visualize the discrepancies among  the noisy and denoised NSST coefficients. Here,\nthe method noise process was applied to capture residuals or any distortions\nintroduced during the CT image denoising process. The deep CNN,28<\/sup> network\narchitecture is applied to method noise to learn complex noise patterns in\norder to capture intricate details effectively and reduce noise components.\nFinally, residual learning denoised image was combined with the NSST high\nfrequency thresholded denoised image to acquire the final denoised CT-image.\nThe final restored image preserves fine details and structural information\nwhile simultaneously removing noise and other artifacts.<\/p>\n\n\n\n

Results and Discussion<\/strong><\/p>\n\n\n\n

The exploratory evaluation is carried out on noisy grayscale CT images with pixel\u2019s size 512×512.  Initially, CT scan test images are obtained from “large COVID-19 CT-scan slice dataset” to determine the efficacy of the suggested denoising method. The Noise-free or clean CT images are required as a reference image to analyse the denoising method’s performance. Fig. 3. is considered as CT images 1, 2,3, and 4 respectively. Fig. 4. depicts the addition of additive gaussian  with a noise variance of 10. To test the experimental results, Additive-white-gaussian-noise is added at different noise levels(\ud835\udf0e = 5, 10, 15, 20) to analyze the effectiveness of various denoising techniques and assess the qualitative performance of noisy CT images.<\/p>\n\n\n\n

Quantitative Evaluation Metrics<\/strong><\/p>\n\n\n\n

The qualitative result analysis of\nthe suggested methodology uses diverse quality factors , i.e., PSNR, SNR, SSIM,\nED, and UIQI,10,41<\/sup>.<\/p>\n\n\n\n

PSNR (Peak Signal-to-Noise ratio)\nis used to assess the quality of restored images relative to the original\nimages. PSNR evaluates the ratio between the given maximum signal strength and\nthe power of distorted noise, i.e., the difference between the clean image and filtered\nimage. For the input CT image X and the denoised CT image Y.<\/p>\n\n\n\n

PSNR\nis denoted as<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Where\nMSE represents the mean-square-error between the original image and the\ndenoised CT image.<\/p>\n\n\n\n

X\n(i, j) depicts the clean CT image.<\/p>\n\n\n\n

Y\n(i, j) depicts the filtered CT image.<\/p>\n\n\n\n

m x n represents\nthe pixel’s size of clean CT image and a denoised CT image.<\/p>\n\n\n\n

(SNR)\nSignal-to-Noise ratio is a qualitative metric to measure and quantify the\ndesired signal strength related to the distortion or noise level. It is\nmeasured in the form of decibels, and it is also used to analyze the image\nquality.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

SSIM (Structural-Similarity-Index-Measure) is\na metric serves as a measure to evaluate the similarity among two images. It is\nmainly relying on three parameters: luminance, contrast, and structural\nfeatures, and the SSIM values vary between -1 and 1, where 1 denotes absolute\nsimilarity and -1 denotes discrepancy between two images.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

X\nrepresents clean CT image.<\/p>\n\n\n\n

Y represents denoised or filtered CT image. <\/p>\n\n\n\n

\u00b5X<\/sub> and \u00b5Y<\/sub> are denoted as the local means, \u03c3X<\/sub>, \u03c3Y<\/sub> are denoted as standard deviations, and \u03c3XY<\/sub><\/em> is image\u2019s covariance of  X and Y Here, C1=(k1D)2<\/sup><\/em>, C2= (k2D)2<\/sup><\/em> are constant values to stabilize division with zeros, where D is the variation in pixel values between 2bits-per-pixel<\/sup><\/em> -1 and 1. Here, k1= 0.01 & k2 = 0.03.<\/p>\n\n\n\n

The Entropy Difference is the statistical\nmeasure of randomness present in an image suitable for analyzing the texture of\nthe given source images. Shannon entropy is estimated between the clean image\n(Xi<\/sub>) and the denoised-CT image (Yi<\/sub>). The dissimilarity in\nthe mean value is denoted as ED.<\/p>\n\n\n\n

ED is computed as:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Where,\nSE denotes Shannon Entropy.<\/p>\n\n\n\n

Shannon Entropy is computed as:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

UIQI\n(Universal-Image-Quality-Index) is a benchmark used to determine the quality of\na denoised CT image and its corresponding reference image.<\/p>\n\n\n\n

The\nUIQI between two images original image distorted image is defined as:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u03bcX<\/sub> \u03bcY<\/sub> represents the average values of the given CT images X and Y.<\/p>\n\n\n\n

\u03c3x<\/sub>2<\/sup><\/em> and \u03c3y<\/sub>2<\/sup><\/em>denotes the variances of X and Y.<\/p>\n\n\n\n

\u03c3XY<\/sub> represents the covariance of the images X and Y. <\/p>\n\n\n\n\n\n
\"\"<\/td>\n\n

Figure 3: <\/strong>Clean CT image dataset : (a) CT1 image, (b) CT2 image, (c) CT3 image, (d) CT4 image.<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
\"\"<\/td>\n\n

Figure 4: <\/strong>Noisy CT image database <\/strong> (a) CT1 image; (b) CT2 image;  (c) CT3 image; (a)CT4 image.<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n

Table 1: PSNR Comparison for the proposed methodology with wiener, median, bilateral, DWT, curvelet transform, contourlet transform, and DnCNN for CT1, CT2, CT3, and CT4 images at various gaussian noise variances (\ud835\udf0e=5, 10, 15, 20 of noise intensity).<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

CT Image<\/strong><\/p>\n<\/td>\n

\n

\ud835\udf0e<\/strong><\/p>\n<\/td>\n

\n

PSNR<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

CT Image<\/strong><\/p>\n<\/td>\n

\n

PSNR<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

5<\/p>\n<\/td>\n

\n

10<\/p>\n<\/td>\n

\n

15<\/p>\n<\/td>\n

\n

20<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

5<\/p>\n<\/td>\n

\n

10<\/p>\n<\/td>\n

\n

15<\/p>\n<\/td>\n

\n

20<\/p>\n<\/td>\n<\/tr>\n

\n

CT 1<\/p>\n<\/td>\n

\n

Wiener filter9<\/sup><\/p>\n<\/td>\n

\n

26.9227<\/p>\n<\/td>\n

\n

21.0561<\/p>\n<\/td>\n

\n

17.1016<\/p>\n<\/td>\n

\n

15.9510<\/p>\n<\/td>\n

\n

CT 2<\/p>\n<\/td>\n

\n

28.8351<\/p>\n<\/td>\n

\n

22.3409<\/p>\n<\/td>\n

\n

20.0957<\/p>\n<\/td>\n

\n

18.0717<\/p>\n<\/td>\n<\/tr>\n

\n

512×512<\/p>\n<\/td>\n

\n

Median filter6<\/sup><\/p>\n<\/td>\n

\n

25.4818<\/p>\n<\/td>\n

\n

21.2815<\/p>\n<\/td>\n

\n

18.0291<\/p>\n<\/td>\n

\n

16.1741<\/p>\n<\/td>\n

\n

512×512<\/p>\n<\/td>\n

\n

26.8228<\/p>\n<\/td>\n

\n

22.6641<\/p>\n<\/td>\n

\n

19.3134<\/p>\n<\/td>\n

\n

17.7229<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Bilateral filter7<\/sup><\/p>\n<\/td>\n

\n

25.8456<\/p>\n<\/td>\n

\n

20.9348<\/p>\n<\/td>\n

\n

18.3621<\/p>\n<\/td>\n

\n

15.5553<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

28.2931<\/p>\n<\/td>\n

\n

22.3078<\/p>\n<\/td>\n

\n

19.6007<\/p>\n<\/td>\n

\n

17.4489<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

NSST with Bivariate17<\/sup><\/p>\n<\/td>\n

\n

35.0639<\/p>\n<\/td>\n

\n

29.4426<\/p>\n<\/td>\n

\n

26.1123<\/p>\n<\/td>\n

\n

23.7630<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

34.9416<\/p>\n<\/td>\n

\n

29.2023<\/p>\n<\/td>\n

\n

25.8483<\/p>\n<\/td>\n

\n

23.5604<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DWT11<\/sup><\/p>\n<\/td>\n

\n

36.1510<\/p>\n<\/td>\n

\n

31.7197<\/p>\n<\/td>\n

\n

28.9528<\/p>\n<\/td>\n

\n

27.1211<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

36.8484<\/p>\n<\/td>\n

\n

32.4378<\/p>\n<\/td>\n

\n

29.6757<\/p>\n<\/td>\n

\n

27.8361<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Curvelet transform12<\/sup><\/p>\n<\/td>\n

\n

24.7381<\/p>\n<\/td>\n

\n

17.8315<\/p>\n<\/td>\n

\n

15.2633<\/p>\n<\/td>\n

\n

15.2232<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

24.4989<\/p>\n<\/td>\n

\n

17.8109<\/p>\n<\/td>\n

\n

15.2434<\/p>\n<\/td>\n

\n

15.3776<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Contourlet transform13<\/sup><\/p>\n<\/td>\n

\n

31.1441<\/p>\n<\/td>\n

\n

28.4641<\/p>\n<\/td>\n

\n

27.7560<\/p>\n<\/td>\n

\n

27.4756<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

31.9356<\/p>\n<\/td>\n

\n

29.3965<\/p>\n<\/td>\n

\n

28.6934<\/p>\n<\/td>\n

\n

28.5351<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DnCNN28<\/sup><\/p>\n<\/td>\n

\n

26.9654<\/p>\n<\/td>\n

\n

21.3395<\/p>\n<\/td>\n

\n

17.8176<\/p>\n<\/td>\n

\n

16.1083<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

27.1848<\/p>\n<\/td>\n

\n

23.4148<\/p>\n<\/td>\n

\n

19.8904<\/p>\n<\/td>\n

\n

17.8606<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Proposed
method<\/p>\n<\/td>\n

\n

38.6875<\/p>\n<\/td>\n

\n

35.4432<\/p>\n<\/td>\n

\n

33.5507<\/p>\n<\/td>\n

\n

32.0938<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

39.3028<\/p>\n<\/td>\n

\n

35.7841<\/p>\n<\/td>\n

\n

33.6865<\/p>\n<\/td>\n

\n

32.2141<\/p>\n<\/td>\n<\/tr>\n

\n

CT 3<\/p>\n<\/td>\n

\n

Wiener filter9<\/sup><\/p>\n<\/td>\n

\n

27.2958<\/p>\n<\/td>\n

\n

21.5341<\/p>\n<\/td>\n

\n

18.9843<\/p>\n<\/td>\n

\n

15.5837<\/p>\n<\/td>\n

\n

CT 4<\/p>\n<\/td>\n

\n

30.4803<\/p>\n<\/td>\n

\n

24.1262<\/p>\n<\/td>\n

\n

20.8647<\/p>\n<\/td>\n

\n

19.7389<\/p>\n<\/td>\n<\/tr>\n

\n

512×512<\/p>\n<\/td>\n

\n

Median filter6<\/sup><\/p>\n<\/td>\n

\n

27.6440<\/p>\n<\/td>\n

\n

20.3498<\/p>\n<\/td>\n

\n

17.9301<\/p>\n<\/td>\n

\n

16.7986<\/p>\n<\/td>\n

\n

512×512<\/p>\n<\/td>\n

\n

29.9581<\/p>\n<\/td>\n

\n

24.2495<\/p>\n<\/td>\n

\n

20.9963<\/p>\n<\/td>\n

\n

19.8384<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Bilateral filter7<\/sup><\/p>\n<\/td>\n

\n

27.4662<\/p>\n<\/td>\n

\n

21.0894<\/p>\n<\/td>\n

\n

18.3180<\/p>\n<\/td>\n

\n

16.2724<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

31.6511<\/p>\n<\/td>\n

\n

24.4505<\/p>\n<\/td>\n

\n

20.8721<\/p>\n<\/td>\n

\n

19.4807<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

NSST with Bivariate17<\/sup><\/p>\n<\/td>\n

\n

34.6530<\/p>\n<\/td>\n

\n

28.8408<\/p>\n<\/td>\n

\n

25.4758<\/p>\n<\/td>\n

\n

23.1329<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

34.5294<\/p>\n<\/td>\n

\n

28.9670<\/p>\n<\/td>\n

\n

25.8372<\/p>\n<\/td>\n

\n

23.6112<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DWT11<\/sup><\/p>\n<\/td>\n

\n

37.7380<\/p>\n<\/td>\n

\n

32.8812<\/p>\n<\/td>\n

\n

30.1778<\/p>\n<\/td>\n

\n

27.9877<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

35.9373<\/p>\n<\/td>\n

\n

31.3968<\/p>\n<\/td>\n

\n

28.6151<\/p>\n<\/td>\n

\n

26.5497<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Curvelet transform12<\/sup><\/p>\n<\/td>\n

\n

24.1199<\/p>\n<\/td>\n

\n

17.7353<\/p>\n<\/td>\n

\n

15.3748<\/p>\n<\/td>\n

\n

15.5832<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

24.6752<\/p>\n<\/td>\n

\n

18.2605<\/p>\n<\/td>\n

\n

15.7387<\/p>\n<\/td>\n

\n

15.7257<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Contourlet transform13<\/sup><\/p>\n<\/td>\n

\n

31.2001<\/p>\n<\/td>\n

\n

28.7470<\/p>\n<\/td>\n

\n

28.1473<\/p>\n<\/td>\n

\n

27.9475<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

32.1699<\/p>\n<\/td>\n

\n

30.3563<\/p>\n<\/td>\n

\n

30.0802<\/p>\n<\/td>\n

\n

30.2322<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DnCNN28<\/sup><\/p>\n<\/td>\n

\n

25.5178<\/p>\n<\/td>\n

\n

21.4493<\/p>\n<\/td>\n

\n

19.0634<\/p>\n<\/td>\n

\n

16.3844<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

30.2987<\/p>\n<\/td>\n

\n

25.0755<\/p>\n<\/td>\n

\n

22.3263<\/p>\n<\/td>\n

\n

19.9453<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Proposed
method<\/p>\n<\/td>\n

\n

40.0415<\/p>\n<\/td>\n

\n

37.0541<\/p>\n<\/td>\n

\n

35.2108<\/p>\n<\/td>\n

\n

33.7444<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

38.7044<\/p>\n<\/td>\n

\n

35.1286<\/p>\n<\/td>\n

\n

33.1462<\/p>\n<\/td>\n

\n

31.7048<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n

Table 2: SNR comparison for the suggested approach with wiener, median, bilateral, DWT, curvelet transform, contourlet transform, and DnCNN for CT1, CT2, CT3, and CT4 images at various gaussian noise variances (\ud835\udf0e=5, 10, 15, 20 of noise intensity).<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

CT Image<\/strong><\/p>\n<\/td>\n

\n

\ud835\udf0e<\/strong><\/p>\n<\/td>\n

\n

SNR<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

CT Image<\/strong><\/p>\n<\/td>\n

\n

SNR<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

5<\/strong><\/p>\n<\/td>\n

\n

10<\/strong><\/p>\n<\/td>\n

\n

15<\/strong><\/p>\n<\/td>\n

\n

20<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

5<\/strong><\/p>\n<\/td>\n

\n

10<\/strong><\/p>\n<\/td>\n

\n

15<\/strong><\/p>\n<\/td>\n

\n

20<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

CT 1<\/p>\n<\/td>\n

\n

Wiener
filter 9<\/sup><\/p>\n<\/td>\n

\n

23.1806<\/p>\n<\/td>\n

\n

17.3140<\/p>\n<\/td>\n

\n

13.3595<\/p>\n<\/td>\n

\n

12.2089<\/p>\n<\/td>\n

\n

CT 2<\/p>\n<\/td>\n

\n

24.3356<\/p>\n<\/td>\n

\n

17.8414<\/p>\n<\/td>\n

\n

15.5962<\/p>\n<\/td>\n

\n

13.5722<\/p>\n<\/td>\n<\/tr>\n

\n

512×512<\/p>\n<\/td>\n

\n

Median
filter6<\/sup><\/p>\n<\/td>\n

\n

21.7397<\/p>\n<\/td>\n

\n

17.5394<\/p>\n<\/td>\n

\n

14.2870<\/p>\n<\/td>\n

\n

12.4320<\/p>\n<\/td>\n

\n

512×512<\/p>\n<\/td>\n

\n

22.3233<\/p>\n<\/td>\n

\n

18.1646<\/p>\n<\/td>\n

\n

14.8139<\/p>\n<\/td>\n

\n

13.2234<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Bilateral
filter7<\/sup><\/p>\n<\/td>\n

\n

22.1035<\/p>\n<\/td>\n

\n

17.1927<\/p>\n<\/td>\n

\n

14.6200<\/p>\n<\/td>\n

\n

11.8132<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

23.7936<\/p>\n<\/td>\n

\n

17.8083<\/p>\n<\/td>\n

\n

15.1012<\/p>\n<\/td>\n

\n

12.9494<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

NSST with Bivariate17<\/sup><\/p>\n<\/td>\n

\n

31.3218<\/p>\n<\/td>\n

\n

25.7005<\/p>\n<\/td>\n

\n

22.3702<\/p>\n<\/td>\n

\n

20.0209<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

30.4421<\/p>\n<\/td>\n

\n

24.7028<\/p>\n<\/td>\n

\n

21.3488<\/p>\n<\/td>\n

\n

19.0609<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DWT11<\/sup><\/p>\n<\/td>\n

\n

32.4093<\/p>\n<\/td>\n

\n

27.9826<\/p>\n<\/td>\n

\n

25.2195<\/p>\n<\/td>\n

\n

23.3900<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

32.3488<\/p>\n<\/td>\n

\n

27.9392<\/p>\n<\/td>\n

\n

25.1814<\/p>\n<\/td>\n

\n

23.3493<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Curvelet transform12<\/sup><\/p>\n<\/td>\n

\n

20.8339<\/p>\n<\/td>\n

\n

13.7838<\/p>\n<\/td>\n

\n

11.1153<\/p>\n<\/td>\n

\n

10.9738<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

19.9783<\/p>\n<\/td>\n

\n

13.2432<\/p>\n<\/td>\n

\n

10.6259<\/p>\n<\/td>\n

\n

10.6641<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Contourlet transform13<\/sup><\/p>\n<\/td>\n

\n

21.0065<\/p>\n<\/td>\n

\n

14.0935<\/p>\n<\/td>\n

\n

11.5272<\/p>\n<\/td>\n

\n

11.3866<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

19.9740<\/p>\n<\/td>\n

\n

13.2892<\/p>\n<\/td>\n

\n

10.8254<\/p>\n<\/td>\n

\n

10.8066<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DnCNN28<\/sup><\/p>\n<\/td>\n

\n

23.2233<\/p>\n<\/td>\n

\n

17.5974<\/p>\n<\/td>\n

\n

14.0755<\/p>\n<\/td>\n

\n

12.3663<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

22.6853<\/p>\n<\/td>\n

\n

18.9153<\/p>\n<\/td>\n

\n

15.3909<\/p>\n<\/td>\n

\n

13.3611<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Proposed
method<\/p>\n<\/td>\n

\n

34.9454<\/p>\n<\/td>\n

\n

31.7011<\/p>\n<\/td>\n

\n

29.8086<\/p>\n<\/td>\n

\n

28.3517<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

34.8033<\/p>\n<\/td>\n

\n

31.2846<\/p>\n<\/td>\n

\n

29.1870<\/p>\n<\/td>\n

\n

27.7154<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n<\/tr>\n

\n

CT 3<\/p>\n<\/td>\n

\n

Wiener
filter9<\/sup><\/p>\n<\/td>\n

\n

24.3152<\/p>\n<\/td>\n

\n

18.5534<\/p>\n<\/td>\n

\n

16.0036<\/p>\n<\/td>\n

\n

12.6031<\/p>\n<\/td>\n

\n

CT 4<\/p>\n<\/td>\n

\n

24.7123<\/p>\n<\/td>\n

\n

18.3583<\/p>\n<\/td>\n

\n

15.0967<\/p>\n<\/td>\n

\n

13.9709<\/p>\n<\/td>\n<\/tr>\n

\n

512×512<\/p>\n<\/td>\n

\n

Median
filter6<\/sup><\/p>\n<\/td>\n

\n

24.6634<\/p>\n<\/td>\n

\n

17.3691<\/p>\n<\/td>\n

\n

14.9494<\/p>\n<\/td>\n

\n

13.8179<\/p>\n<\/td>\n

\n

512×512<\/p>\n<\/td>\n

\n

24.1901<\/p>\n<\/td>\n

\n

18.4815<\/p>\n<\/td>\n

\n

15.2284<\/p>\n<\/td>\n

\n

14.0705<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Bilateral
filter7<\/sup><\/p>\n<\/td>\n

\n

24.4855<\/p>\n<\/td>\n

\n

18.1087<\/p>\n<\/td>\n

\n

15.3373<\/p>\n<\/td>\n

\n

13.2917<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

25.8831<\/p>\n<\/td>\n

\n

18.6825<\/p>\n<\/td>\n

\n

15.1041<\/p>\n<\/td>\n

\n

13.7127<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

NSST with Bivariate17<\/sup><\/p>\n<\/td>\n

\n

31.6724<\/p>\n<\/td>\n

\n

25.8601<\/p>\n<\/td>\n

\n

22.4952<\/p>\n<\/td>\n

\n

25.1522<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

28.7614<\/p>\n<\/td>\n

\n

23.1990<\/p>\n<\/td>\n

\n

20.0692<\/p>\n<\/td>\n

\n

17.8432<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DWT11<\/sup><\/p>\n<\/td>\n

\n

34.7583<\/p>\n<\/td>\n

\n

29.9035<\/p>\n<\/td>\n

\n

27.2033<\/p>\n<\/td>\n

\n

25.0127<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

30.1727<\/p>\n<\/td>\n

\n

25.6366<\/p>\n<\/td>\n

\n

22.8592<\/p>\n<\/td>\n

\n

20.7994<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Curvelet transform12<\/sup><\/p>\n<\/td>\n

\n

21.1356<\/p>\n<\/td>\n

\n

14.6744<\/p>\n<\/td>\n

\n

12.1857<\/p>\n<\/td>\n

\n

12.2720<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

18.9421<\/p>\n<\/td>\n

\n

12.6007<\/p>\n<\/td>\n

\n

10.0722<\/p>\n<\/td>\n

\n

09.9956<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Contourlet transform13<\/sup><\/p>\n<\/td>\n

\n

21.0577<\/p>\n<\/td>\n

\n

14.7171<\/p>\n<\/td>\n

\n

12.4321<\/p>\n<\/td>\n

\n

12.5608<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

18.8854<\/p>\n<\/td>\n

\n

12.5286<\/p>\n<\/td>\n

\n

09.9644<\/p>\n<\/td>\n

\n

09.9185<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DnCNN28<\/sup><\/p>\n<\/td>\n

\n

22.5371<\/p>\n<\/td>\n

\n

18.4687<\/p>\n<\/td>\n

\n

16.0827<\/p>\n<\/td>\n

\n

14.4038<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

24.5307<\/p>\n<\/td>\n

\n

19.3075<\/p>\n<\/td>\n

\n

16.5583<\/p>\n<\/td>\n

\n

14.1773<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Proposed
method<\/p>\n<\/td>\n

\n

37.0609<\/p>\n<\/td>\n

\n

34.0742<\/p>\n<\/td>\n

\n

32.2301<\/p>\n<\/td>\n

\n

30.7637<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

32.9364<\/p>\n<\/td>\n

\n

29.6594<\/p>\n<\/td>\n

\n

27.3780<\/p>\n<\/td>\n

\n

25.9118<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n

Table 3: SSIM comparison for the proposed ensembled approach with wiener, median, bilateral, DWT, curvelet transform, contourlet transform, and DnCNN for CT1, CT2, CT3, and CT4 images at various gaussian noise variances (\ud835\udf0e=5, 10, 15, 20 of noise intensity).<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

CT Image<\/strong><\/p>\n<\/td>\n

\n

\ud835\udf0e<\/strong><\/p>\n<\/td>\n

\n

SNR<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

CT Image<\/strong><\/p>\n<\/td>\n

\n

SNR<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

5<\/strong><\/p>\n<\/td>\n

\n

10<\/strong><\/p>\n<\/td>\n

\n

15<\/strong><\/p>\n<\/td>\n

\n

20<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

5<\/strong><\/p>\n<\/td>\n

\n

10<\/strong><\/p>\n<\/td>\n

\n

15<\/strong><\/p>\n<\/td>\n

\n

20<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

CT 1<\/p>\n<\/td>\n

\n

Wiener
filter 9<\/sup><\/p>\n<\/td>\n

\n

23.1806<\/p>\n<\/td>\n

\n

17.3140<\/p>\n<\/td>\n

\n

13.3595<\/p>\n<\/td>\n

\n

12.2089<\/p>\n<\/td>\n

\n

CT 2<\/p>\n<\/td>\n

\n

24.3356<\/p>\n<\/td>\n

\n

17.8414<\/p>\n<\/td>\n

\n

15.5962<\/p>\n<\/td>\n

\n

13.5722<\/p>\n<\/td>\n<\/tr>\n

\n

512×512<\/p>\n<\/td>\n

\n

Median
filter6<\/sup><\/p>\n<\/td>\n

\n

21.7397<\/p>\n<\/td>\n

\n

17.5394<\/p>\n<\/td>\n

\n

14.2870<\/p>\n<\/td>\n

\n

12.4320<\/p>\n<\/td>\n

\n

512×512<\/p>\n<\/td>\n

\n

22.3233<\/p>\n<\/td>\n

\n

18.1646<\/p>\n<\/td>\n

\n

14.8139<\/p>\n<\/td>\n

\n

13.2234<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Bilateral
filter7<\/sup><\/p>\n<\/td>\n

\n

22.1035<\/p>\n<\/td>\n

\n

17.1927<\/p>\n<\/td>\n

\n

14.6200<\/p>\n<\/td>\n

\n

11.8132<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

23.7936<\/p>\n<\/td>\n

\n

17.8083<\/p>\n<\/td>\n

\n

15.1012<\/p>\n<\/td>\n

\n

12.9494<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

NSST with Bivariate17<\/sup><\/p>\n<\/td>\n

\n

31.3218<\/p>\n<\/td>\n

\n

25.7005<\/p>\n<\/td>\n

\n

22.3702<\/p>\n<\/td>\n

\n

20.0209<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

30.4421<\/p>\n<\/td>\n

\n

24.7028<\/p>\n<\/td>\n

\n

21.3488<\/p>\n<\/td>\n

\n

19.0609<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DWT11<\/sup><\/p>\n<\/td>\n

\n

32.4093<\/p>\n<\/td>\n

\n

27.9826<\/p>\n<\/td>\n

\n

25.2195<\/p>\n<\/td>\n

\n

23.3900<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

32.3488<\/p>\n<\/td>\n

\n

27.9392<\/p>\n<\/td>\n

\n

25.1814<\/p>\n<\/td>\n

\n

23.3493<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Curvelet transform12<\/sup><\/p>\n<\/td>\n

\n

20.8339<\/p>\n<\/td>\n

\n

13.7838<\/p>\n<\/td>\n

\n

11.1153<\/p>\n<\/td>\n

\n

10.9738<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

19.9783<\/p>\n<\/td>\n

\n

13.2432<\/p>\n<\/td>\n

\n

10.6259<\/p>\n<\/td>\n

\n

10.6641<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Contourlet transform13<\/sup><\/p>\n<\/td>\n

\n

21.0065<\/p>\n<\/td>\n

\n

14.0935<\/p>\n<\/td>\n

\n

11.5272<\/p>\n<\/td>\n

\n

11.3866<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

19.9740<\/p>\n<\/td>\n

\n

13.2892<\/p>\n<\/td>\n

\n

10.8254<\/p>\n<\/td>\n

\n

10.8066<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DnCNN28<\/sup><\/p>\n<\/td>\n

\n

23.2233<\/p>\n<\/td>\n

\n

17.5974<\/p>\n<\/td>\n

\n

14.0755<\/p>\n<\/td>\n

\n

12.3663<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

22.6853<\/p>\n<\/td>\n

\n

18.9153<\/p>\n<\/td>\n

\n

15.3909<\/p>\n<\/td>\n

\n

13.3611<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Proposed
method<\/p>\n<\/td>\n

\n

34.9454<\/p>\n<\/td>\n

\n

31.7011<\/p>\n<\/td>\n

\n

29.8086<\/p>\n<\/td>\n

\n

28.3517<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

34.8033<\/p>\n<\/td>\n

\n

31.2846<\/p>\n<\/td>\n

\n

29.1870<\/p>\n<\/td>\n

\n

27.7154<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n<\/tr>\n

\n

CT 3<\/p>\n<\/td>\n

\n

Wiener
filter9<\/sup><\/p>\n<\/td>\n

\n

24.3152<\/p>\n<\/td>\n

\n

18.5534<\/p>\n<\/td>\n

\n

16.0036<\/p>\n<\/td>\n

\n

12.6031<\/p>\n<\/td>\n

\n

CT 4<\/p>\n<\/td>\n

\n

24.7123<\/p>\n<\/td>\n

\n

18.3583<\/p>\n<\/td>\n

\n

15.0967<\/p>\n<\/td>\n

\n

13.9709<\/p>\n<\/td>\n<\/tr>\n

\n

512×512<\/p>\n<\/td>\n

\n

Median
filter6<\/sup><\/p>\n<\/td>\n

\n

24.6634<\/p>\n<\/td>\n

\n

17.3691<\/p>\n<\/td>\n

\n

14.9494<\/p>\n<\/td>\n

\n

13.8179<\/p>\n<\/td>\n

\n

512×512<\/p>\n<\/td>\n

\n

24.1901<\/p>\n<\/td>\n

\n

18.4815<\/p>\n<\/td>\n

\n

15.2284<\/p>\n<\/td>\n

\n

14.0705<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Bilateral
filter7<\/sup><\/p>\n<\/td>\n

\n

24.4855<\/p>\n<\/td>\n

\n

18.1087<\/p>\n<\/td>\n

\n

15.3373<\/p>\n<\/td>\n

\n

13.2917<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

25.8831<\/p>\n<\/td>\n

\n

18.6825<\/p>\n<\/td>\n

\n

15.1041<\/p>\n<\/td>\n

\n

13.7127<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

NSST with Bivariate17<\/sup><\/p>\n<\/td>\n

\n

31.6724<\/p>\n<\/td>\n

\n

25.8601<\/p>\n<\/td>\n

\n

22.4952<\/p>\n<\/td>\n

\n

25.1522<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

28.7614<\/p>\n<\/td>\n

\n

23.1990<\/p>\n<\/td>\n

\n

20.0692<\/p>\n<\/td>\n

\n

17.8432<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DWT11<\/sup><\/p>\n<\/td>\n

\n

34.7583<\/p>\n<\/td>\n

\n

29.9035<\/p>\n<\/td>\n

\n

27.2033<\/p>\n<\/td>\n

\n

25.0127<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

30.1727<\/p>\n<\/td>\n

\n

25.6366<\/p>\n<\/td>\n

\n

22.8592<\/p>\n<\/td>\n

\n

20.7994<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Curvelet transform12<\/sup><\/p>\n<\/td>\n

\n

21.1356<\/p>\n<\/td>\n

\n

14.6744<\/p>\n<\/td>\n

\n

12.1857<\/p>\n<\/td>\n

\n

12.2720<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

18.9421<\/p>\n<\/td>\n

\n

12.6007<\/p>\n<\/td>\n

\n

10.0722<\/p>\n<\/td>\n

\n

09.9956<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Contourlet transform13<\/sup><\/p>\n<\/td>\n

\n

21.0577<\/p>\n<\/td>\n

\n

14.7171<\/p>\n<\/td>\n

\n

12.4321<\/p>\n<\/td>\n

\n

12.5608<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

18.8854<\/p>\n<\/td>\n

\n

12.5286<\/p>\n<\/td>\n

\n

09.9644<\/p>\n<\/td>\n

\n

09.9185<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DnCNN28<\/sup><\/p>\n<\/td>\n

\n

22.5371<\/p>\n<\/td>\n

\n

18.4687<\/p>\n<\/td>\n

\n

16.0827<\/p>\n<\/td>\n

\n

14.4038<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

24.5307<\/p>\n<\/td>\n

\n

19.3075<\/p>\n<\/td>\n

\n

16.5583<\/p>\n<\/td>\n

\n

14.1773<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Proposed
method<\/p>\n<\/td>\n

\n

37.0609<\/p>\n<\/td>\n

\n

34.0742<\/p>\n<\/td>\n

\n

32.2301<\/p>\n<\/td>\n

\n

30.7637<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

32.9364<\/p>\n<\/td>\n

\n

29.6594<\/p>\n<\/td>\n

\n

27.3780<\/p>\n<\/td>\n

\n

25.9118<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n

Table 4: ED Comparison for the proposed approach with wiener, median, bilateral, DWT, curvelet transform, contourlet transform, and DnCNN for CT1, CT2, CT3, and CT4 images at various gaussian noise variances (\ud835\udf0e=5, 10, 15, 20 of noise intensity).<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

CT Image<\/strong><\/p>\n<\/td>\n

\n

\ud835\udf0e<\/strong><\/p>\n<\/td>\n

\n

ED<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

CT Image<\/strong><\/p>\n<\/td>\n

\n

ED<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

5<\/strong><\/p>\n<\/td>\n

\n

10<\/strong><\/p>\n<\/td>\n

\n

15<\/strong><\/p>\n<\/td>\n

\n

20<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

5<\/strong><\/p>\n<\/td>\n

\n

10<\/strong><\/p>\n<\/td>\n

\n

15<\/strong><\/p>\n<\/td>\n

\n

20<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

CT 1<\/p>\n<\/td>\n

\n

Wiener
filter9<\/sup><\/p>\n<\/td>\n

\n

0.2614<\/p>\n<\/td>\n

\n

0.4414<\/p>\n<\/td>\n

\n

0.5418<\/p>\n<\/td>\n

\n

0.6709<\/p>\n<\/td>\n

\n

CT 2<\/p>\n<\/td>\n

\n

0.2177<\/p>\n<\/td>\n

\n

0.3527<\/p>\n<\/td>\n

\n

0.4904<\/p>\n<\/td>\n

\n

0.5725<\/p>\n<\/td>\n<\/tr>\n

\n

512×512<\/p>\n<\/td>\n

\n

Median
filter6<\/sup><\/p>\n<\/td>\n

\n

0.2170<\/p>\n<\/td>\n

\n

0.4034<\/p>\n<\/td>\n

\n

0.5029<\/p>\n<\/td>\n

\n

0.5559<\/p>\n<\/td>\n

\n

512×512<\/p>\n<\/td>\n

\n

0.2219<\/p>\n<\/td>\n

\n

0.3135<\/p>\n<\/td>\n

\n

0.3555<\/p>\n<\/td>\n

\n

0.4014<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Bilateral
filter7<\/sup><\/p>\n<\/td>\n

\n

0.1795<\/p>\n<\/td>\n

\n

0.4045<\/p>\n<\/td>\n

\n

0.5949<\/p>\n<\/td>\n

\n

0.7027<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.1673<\/p>\n<\/td>\n

\n

0.3201<\/p>\n<\/td>\n

\n

0.4543<\/p>\n<\/td>\n

\n

0.5704<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

NSST with Bivariate17<\/sup><\/p>\n<\/td>\n

\n

0.4774<\/p>\n<\/td>\n

\n

0.7059<\/p>\n<\/td>\n

\n

0.8858<\/p>\n<\/td>\n

\n

1.0016<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.5220<\/p>\n<\/td>\n

\n

0.7635<\/p>\n<\/td>\n

\n

0.9367<\/p>\n<\/td>\n

\n

1.0175<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DWT11<\/sup><\/p>\n<\/td>\n

\n

0.1864<\/p>\n<\/td>\n

\n

0.0496<\/p>\n<\/td>\n

\n

0.0314<\/p>\n<\/td>\n

\n

0.0524<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.7585<\/p>\n<\/td>\n

\n

0.6040<\/p>\n<\/td>\n

\n

0.5585<\/p>\n<\/td>\n

\n

0.4996<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Curvelet transform12<\/sup><\/p>\n<\/td>\n

\n

0.5713<\/p>\n<\/td>\n

\n

0.5397<\/p>\n<\/td>\n

\n

0.5113<\/p>\n<\/td>\n

\n

0.5491<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.5713<\/p>\n<\/td>\n

\n

0.5397<\/p>\n<\/td>\n

\n

0.5113<\/p>\n<\/td>\n

\n

0.5491<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Contourlet transform13<\/sup><\/p>\n<\/td>\n

\n

0.5716<\/p>\n<\/td>\n

\n

0.5356<\/p>\n<\/td>\n

\n

0.5147<\/p>\n<\/td>\n

\n

0.5532<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.0596<\/p>\n<\/td>\n

\n

0.0004<\/p>\n<\/td>\n

\n

0.0272<\/p>\n<\/td>\n

\n

0.0219<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DnCNN28<\/sup><\/p>\n<\/td>\n

\n

0.2900<\/p>\n<\/td>\n

\n

0.1760<\/p>\n<\/td>\n

\n

0.1220<\/p>\n<\/td>\n

\n

0.0996<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.2331<\/p>\n<\/td>\n

\n

0.1782<\/p>\n<\/td>\n

\n

0.1261<\/p>\n<\/td>\n

\n

0.1137<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Proposed
method<\/p>\n<\/td>\n

\n

0.0383<\/p>\n<\/td>\n

\n

0.0583<\/p>\n<\/td>\n

\n

0.0719<\/p>\n<\/td>\n

\n

0.0841<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.0330<\/p>\n<\/td>\n

\n

0.0550<\/p>\n<\/td>\n

\n

0.0699<\/p>\n<\/td>\n

\n

0.0793<\/p>\n<\/td>\n<\/tr>\n

\n

CT 3<\/p>\n<\/td>\n

\n

Wiener
filter9<\/sup><\/p>\n<\/td>\n

\n

0.0944<\/p>\n<\/td>\n

\n

0.2976<\/p>\n<\/td>\n

\n

0.4661<\/p>\n<\/td>\n

\n

0.4913<\/p>\n<\/td>\n

\n

CT 4<\/p>\n<\/td>\n

\n

0.0019<\/p>\n<\/td>\n

\n

0.0415<\/p>\n<\/td>\n

\n

0.0594<\/p>\n<\/td>\n

\n

0.0611<\/p>\n<\/td>\n<\/tr>\n

\n

512×512<\/p>\n<\/td>\n

\n

Median
filter6<\/sup><\/p>\n<\/td>\n

\n

0.1303<\/p>\n<\/td>\n

\n

0.2915<\/p>\n<\/td>\n

\n

0.3970<\/p>\n<\/td>\n

\n

0.4959<\/p>\n<\/td>\n

\n

512×512<\/p>\n<\/td>\n

\n

0.0165<\/p>\n<\/td>\n

\n

0.1158<\/p>\n<\/td>\n

\n

0.1584<\/p>\n<\/td>\n

\n

0.1983<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Bilateral
filter7<\/sup><\/p>\n<\/td>\n

\n

0.0648<\/p>\n<\/td>\n

\n

0.2603<\/p>\n<\/td>\n

\n

0.4550<\/p>\n<\/td>\n

\n

0.6012<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.0449<\/p>\n<\/td>\n

\n

0.0429<\/p>\n<\/td>\n

\n

0.0566<\/p>\n<\/td>\n

\n

0.1164<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

NSST with Bivariate17<\/sup><\/p>\n<\/td>\n

\n

0.5307<\/p>\n<\/td>\n

\n

0.8390<\/p>\n<\/td>\n

\n

1.0659<\/p>\n<\/td>\n

\n

1.2341<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.3086<\/p>\n<\/td>\n

\n

0.4871<\/p>\n<\/td>\n

\n

0.5824<\/p>\n<\/td>\n

\n

0.6565<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DWT11<\/sup><\/p>\n<\/td>\n

\n

0.0734<\/p>\n<\/td>\n

\n

0.0207<\/p>\n<\/td>\n

\n

0.0020<\/p>\n<\/td>\n

\n

0.0052<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.0342<\/p>\n<\/td>\n

\n

0.0760<\/p>\n<\/td>\n

\n

0.1391<\/p>\n<\/td>\n

\n

0.2021<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Curvelet transform12<\/sup><\/p>\n<\/td>\n

\n

0.2521<\/p>\n<\/td>\n

\n

0.2080<\/p>\n<\/td>\n

\n

0.2045<\/p>\n<\/td>\n

\n

0.2320<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.0490<\/p>\n<\/td>\n

\n

0.1310<\/p>\n<\/td>\n

\n

0.1386<\/p>\n<\/td>\n

\n

0.0825<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Contourlet transform13<\/sup><\/p>\n<\/td>\n

\n

0.2514<\/p>\n<\/td>\n

\n

0.2189<\/p>\n<\/td>\n

\n

0.2108<\/p>\n<\/td>\n

\n

0.2303<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.0511<\/p>\n<\/td>\n

\n

0.1296<\/p>\n<\/td>\n

\n

0.1394<\/p>\n<\/td>\n

\n

0.0881<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DnCNN28<\/sup><\/p>\n<\/td>\n

\n

0.0544<\/p>\n<\/td>\n

\n

0.0314<\/p>\n<\/td>\n

\n

0.0292<\/p>\n<\/td>\n

\n

0.0307<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.0521<\/p>\n<\/td>\n

\n

0.1397<\/p>\n<\/td>\n

\n

0.1617<\/p>\n<\/td>\n

\n

0.1828<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Proposed
method<\/p>\n<\/td>\n

\n

0.0361<\/p>\n<\/td>\n

\n

0.0544<\/p>\n<\/td>\n

\n

0.0772<\/p>\n<\/td>\n

\n

0.0771<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.0204<\/p>\n<\/td>\n

\n

0.0360<\/p>\n<\/td>\n

\n

0.0484<\/p>\n<\/td>\n

\n

0.0587<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n

Table 5: UIQI Comparison for the proposed method with comparison of UIQI values with wiener, median, bilateral, DWT, curvelet transform, contourlet transform, and DnCNN for CT1, CT2, CT3, and CT4 images at various gaussian noise variances (\ud835\udf0e=5, 10, 15, 20 of noise intensity).<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

CT Image<\/strong><\/p>\n<\/td>\n

\n

\ud835\udf0e<\/strong><\/p>\n<\/td>\n

\n

UIQI<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

CT Image<\/strong><\/p>\n<\/td>\n

\n

UIQI<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

5<\/strong><\/p>\n<\/td>\n

\n

10<\/strong><\/p>\n<\/td>\n

\n

15<\/strong><\/p>\n<\/td>\n

\n

20<\/strong><\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

5<\/strong><\/p>\n<\/td>\n

\n

10<\/strong><\/p>\n<\/td>\n

\n

15<\/strong><\/p>\n<\/td>\n

\n

20<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

CT 1<\/p>\n<\/td>\n

\n

Wiener
filter9<\/sup><\/p>\n<\/td>\n

\n

0.9945<\/p>\n<\/td>\n

\n

0.9776<\/p>\n<\/td>\n

\n

0.9412<\/p>\n<\/td>\n

\n

0.9209<\/p>\n<\/td>\n

\n

CT 2<\/p>\n<\/td>\n

\n

0.9958<\/p>\n<\/td>\n

\n

0.9803<\/p>\n<\/td>\n

\n

0.9655<\/p>\n<\/td>\n

\n

0.9430<\/p>\n<\/td>\n<\/tr>\n

\n

512×512<\/p>\n<\/td>\n

\n

Median
filter6<\/sup><\/p>\n<\/td>\n

\n

0.9922<\/p>\n<\/td>\n

\n

0.9792<\/p>\n<\/td>\n

\n

0.9543<\/p>\n<\/td>\n

\n

0.9277<\/p>\n<\/td>\n

\n

512×512<\/p>\n<\/td>\n

\n

0.9935<\/p>\n<\/td>\n

\n

0.9824<\/p>\n<\/td>\n

\n

0.9602<\/p>\n<\/td>\n

\n

0.9408<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Bilateral
filter7<\/sup><\/p>\n<\/td>\n

\n

0.9930<\/p>\n<\/td>\n

\n

0.9700<\/p>\n<\/td>\n

\n

0.9567<\/p>\n<\/td>\n

\n

0.9130<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9953<\/p>\n<\/td>\n

\n

0.9802<\/p>\n<\/td>\n

\n

0.9613<\/p>\n<\/td>\n

\n

0.9339<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

NSST with Bivariate17<\/sup><\/p>\n<\/td>\n

\n

0.9989<\/p>\n<\/td>\n

\n

0.9959<\/p>\n<\/td>\n

\n

0.9910<\/p>\n<\/td>\n

\n

0.9845<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9983<\/p>\n<\/td>\n

\n

0.9949<\/p>\n<\/td>\n

\n

0.9890<\/p>\n<\/td>\n

\n

0.9812<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DWT11<\/sup><\/p>\n<\/td>\n

\n

0.9991<\/p>\n<\/td>\n

\n

0.9976<\/p>\n<\/td>\n

\n

0.9955<\/p>\n<\/td>\n

\n

0.9931<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9991<\/p>\n<\/td>\n

\n

0.9976<\/p>\n<\/td>\n

\n

0.9955<\/p>\n<\/td>\n

\n

0.9932<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Curvelet transform12<\/sup><\/p>\n<\/td>\n

\n

0.9874<\/p>\n<\/td>\n

\n

0.9363<\/p>\n<\/td>\n

\n

0.8822<\/p>\n<\/td>\n

\n

0.8774<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9874<\/p>\n<\/td>\n

\n

0.9363<\/p>\n<\/td>\n

\n

0.8822<\/p>\n<\/td>\n

\n

0.8774<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Contourlet transform13<\/sup><\/p>\n<\/td>\n

\n

0.9874<\/p>\n<\/td>\n

\n

0.9364<\/p>\n<\/td>\n

\n

0.8824<\/p>\n<\/td>\n

\n

0.8746<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9848<\/p>\n<\/td>\n

\n

0.9275<\/p>\n<\/td>\n

\n

0.8696<\/p>\n<\/td>\n

\n

0.8644<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DnCNN28<\/sup><\/p>\n<\/td>\n

\n

0.9947<\/p>\n<\/td>\n

\n

0.9800<\/p>\n<\/td>\n

\n

0.9525<\/p>\n<\/td>\n

\n

0.9272<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9940<\/p>\n<\/td>\n

\n

0.9854<\/p>\n<\/td>\n

\n

0.9656<\/p>\n<\/td>\n

\n

0.9431<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Proposed
method<\/p>\n<\/td>\n

\n

0.9995<\/p>\n<\/td>\n

\n

0.9989<\/p>\n<\/td>\n

\n

0.9984<\/p>\n<\/td>\n

\n

0.9977<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9995<\/p>\n<\/td>\n

\n

0.9989<\/p>\n<\/td>\n

\n

0.9982<\/p>\n<\/td>\n

\n

0.9975<\/p>\n<\/td>\n<\/tr>\n

\n

CT 3<\/p>\n<\/td>\n

\n

Wiener
filter9<\/sup><\/p>\n<\/td>\n

\n

0.9955<\/p>\n<\/td>\n

\n

0.9824<\/p>\n<\/td>\n

\n

0.9667<\/p>\n<\/td>\n

\n

0.9212<\/p>\n<\/td>\n

\n

CT 4<\/p>\n<\/td>\n

\n

0.9963<\/p>\n<\/td>\n

\n

0.9834<\/p>\n<\/td>\n

\n

0.9631<\/p>\n<\/td>\n

\n

0.9510<\/p>\n<\/td>\n<\/tr>\n

\n

512×512<\/p>\n<\/td>\n

\n

Median
filter6<\/sup><\/p>\n<\/td>\n

\n

0.9960<\/p>\n<\/td>\n

\n

0.9779<\/p>\n<\/td>\n

\n

0.9600<\/p>\n<\/td>\n

\n

0.9462<\/p>\n<\/td>\n

\n

512×512<\/p>\n<\/td>\n

\n

0.9958<\/p>\n<\/td>\n

\n

0.9839<\/p>\n<\/td>\n

\n

0.9645<\/p>\n<\/td>\n

\n

0.9527<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Bilateral
filter7<\/sup><\/p>\n<\/td>\n

\n

0.9957<\/p>\n<\/td>\n

\n

0.9807<\/p>\n<\/td>\n

\n

0.9614<\/p>\n<\/td>\n

\n

0.9348<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9972<\/p>\n<\/td>\n

\n

0.9847<\/p>\n<\/td>\n

\n

0.9633<\/p>\n<\/td>\n

\n

0.9479<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

NSST with Bivariate17<\/sup><\/p>\n<\/td>\n

\n

0.9979<\/p>\n<\/td>\n

\n

0.9917<\/p>\n<\/td>\n

\n

0.9820<\/p>\n<\/td>\n

\n

0.9693<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9985<\/p>\n<\/td>\n

\n

0.9946<\/p>\n<\/td>\n

\n

0.9888<\/p>\n<\/td>\n

\n

0.9812<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DWT11<\/sup><\/p>\n<\/td>\n

\n

0.9989<\/p>\n<\/td>\n

\n

0.9967<\/p>\n<\/td>\n

\n

0.9939<\/p>\n<\/td>\n

\n

0.9899<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9989<\/p>\n<\/td>\n

\n

0.9969<\/p>\n<\/td>\n

\n

0.9941<\/p>\n<\/td>\n

\n

0.9906<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Curvelet transform12<\/sup><\/p>\n<\/td>\n

\n

0.9751<\/p>\n<\/td>\n

\n

0.8941<\/p>\n<\/td>\n

\n

0.8200<\/p>\n<\/td>\n

\n

0.8228<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9853<\/p>\n<\/td>\n

\n

0.9346<\/p>\n<\/td>\n

\n

0.8800<\/p>\n<\/td>\n

\n

0.8759<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Contourlet transform 3<\/sup><\/p>\n<\/td>\n

\n

0.9747<\/p>\n<\/td>\n

\n

0.8934<\/p>\n<\/td>\n

\n

0.8291<\/p>\n<\/td>\n

\n

0.8207<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9853<\/p>\n<\/td>\n

\n

0.9350<\/p>\n<\/td>\n

\n

0.8798<\/p>\n<\/td>\n

\n

0.8747<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

DnCNN28<\/sup><\/p>\n<\/td>\n

\n

0.9936<\/p>\n<\/td>\n

\n

0.9833<\/p>\n<\/td>\n

\n

0.9703<\/p>\n<\/td>\n

\n

0.9429<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9962<\/p>\n<\/td>\n

\n

0.9869<\/p>\n<\/td>\n

\n

0.9744<\/p>\n<\/td>\n

\n

0.9540<\/p>\n<\/td>\n<\/tr>\n

\n

 <\/p>\n<\/td>\n

\n

Proposed
method<\/p>\n<\/td>\n

\n

0.9993<\/p>\n<\/td>\n

\n

0.9989<\/p>\n<\/td>\n

\n

0.9981<\/p>\n<\/td>\n

\n

0.9973<\/p>\n<\/td>\n

\n

 <\/p>\n<\/td>\n

\n

0.9994<\/p>\n<\/td>\n

\n

0.9986<\/p>\n<\/td>\n

\n

0.9979<\/p>\n<\/td>\n

\n

0.9971<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n

Visual Evaluation of the Experimental Results with Additive White Gaussian Noise<\/strong><\/p>\n\n\n\n\n\n
\"\"<\/td>\nFigure 5: <\/strong>Outcomes of the Wiener filter [9].<\/strong>

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
\"\"<\/a><\/td>\n\n

Figure 6: <\/strong>Outcomes of the Median filter [6].<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
\"\"<\/td>\n\n

Figure 7: <\/strong>Outcomes of the Bilateral filter [7].<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
\"\"<\/td>\n\n

Figure 8: <\/strong>Outcomes of the NSST with Bivariate shrinkage [17].<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
\"\"<\/td>\n\n

Figure 9:<\/strong> Outcomes of the DWT [11].<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
\"\"<\/td>\n\n

Figure 10: <\/strong>Outcomes of the Curvelet transform [12].<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
\"\"<\/td>\n\n

Figure 11: <\/strong>Outcomes of the Contourlet transform [13].<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
\"\"<\/td>\n\n

Figure 12: <\/strong>Outcomes of the DnCNN [28]<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
\"\"<\/td>\n\n

Figure 13: <\/strong>Outcomes of the Proposed method.<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n

For strong comparison, the noisy CT images are denoised using various approaches, like wiener, median, bilateral, DWT, curvelet transform, contourlet transform, DnCNN, and the proposed method. The performance criteria, including PSNR, SNR, SSIM, ED, and UIQI, are assessed across different noise variances, as presented in Table no. from 1 to 5. The results of the proposed method are highlighted in bold. It is clear from, comparing Tables 1 to 5 that the proposed method outperforms the mentioned standard methods.Table no.1, illustrates comparative analysis of different denoising methods based on PSNR, while Table 2, based on SNR, while Table 3 on SSIM, while Table 4  on ED and Table 5 on UIQI.<\/p>\n\n\n\n

Table no.1 shows PSNR results for different denoising approaches applied to four CT images (CT1, CT2, CT3 and CT4) at various gaussian noise levels (\ud835\udf0e = 5,10,15,20). The PSNR refers how efficiently the signal is preserved in relation to the level to which its representation has been distorted by noise. The higher PSNR values generally indicates better imaging quality. The proposed method proves to be consistently achieving the highest PSNR values among all mentioned methods. For PSNR, a 0.5% increase in noise results in a considerable decrease of 2-5 points in the PSNR value. SNR measures the ratio between intensity of the desired signal and amount of the noise present in the image. For SNR, increase in noise causes substantial reduction of 1-6 points in SNR value as shown in Table no.2. The method consistently delivers the highest SNR value in comparison with other standard denoising methods.<\/p>\n\n\n\n

SSIM is commonly employed to evaluate the imaging quality after compression, denoising, or other processing approaches. It plays a vital role in assessing how well various image denoising algorithms preserve structural information. The SSIM range extends between 0 and 1, with values closer to 1 indicating better denoising performance. For instance, the SSIM values of CT image no. 3 (0.9400) and CT image no. 4 (0.9632) at \ud835\udf0e = 5 are somewhat inferior to those of the proposed method, as shown in Table no.3. CT images with SSIM values greater than 0.80 are considered to be of high quality. It is evident that the proposed method yields superior results compared to existing standard methods in terms of SSIM values.<\/p>\n\n\n\n

Table no.4 presents ED values of various denoising methods. A lower ED indicates that the denoising method has well preserved the features of the clean image. The ED values of the Wiener filter for CT image 2 at noise levels 10, 15, and 20 exhibit inconsistent performance, with the ED11<\/sup> values changing markedly. In CT image 3, the ED7 <\/sup>values of the DWT approach are also quite a bit lower compared to the proposed method at noise levels 10, 15, and 20. However, the difference between the proposed method and the outcomes of other standard approaches is quite small. The proposed method consistently outperforms the other denoising techniques in terms of minimizing entropy difference and preserving the original image’s details across various noise intensity levels.<\/p>\n\n\n\n

Table no.5 shows a detailed comparison of various denoising methods applied on 4 CT images (CT1, CT2, CT3 and CT4) including proposed method based on UIQI values at different gaussian noise levels (\u03c3 = 5,10,15,20). Here, UIQI is used to analyze the quality of denoised-CT images, where higher UIQI value indicates superior image quality. The proposed method performs well at (\ud835\udf0e =5) lower noise levels. The proposed technique achieves the highest UIQI values among all standard methods, with DWT and proposed method exhibiting slightly better performance.<\/p>\n\n\n\n

The exploratory results of, 9<\/sup> as depicted in Fig. 5 are evaluated, and it is noted that the denoising scheme is performed well but does not effectively preserve structural details at higher noise levels. In the experimental data of ,6<\/sup> as illustrated in Fig. 6, it is observed that the noise suppression is performed effectively, but at higher noise levels, it is unable to preserve the image’s smoothness and edge information in detail. According to the experimental results of,7<\/sup> as demonstrated in Fig. 7, the noise suppression is done effectively. The SSIM of CT3 and CT4 images shows better outcomes at noise variance 5. The experimental findings of,17<\/sup> as depicted in Fig. 8, show that noise suppression and other artifacts are reduced successfully, and it is observed that as more noise is added, resulting blurry images.<\/p>\n\n\n\n

In the experimental results of,11<\/sup> as shown in Fig. 9, the noise suppression is performed well, but as the noise increases, it affects image clarity and quality. The experimental outcomes of,12<\/sup> as shown in Fig. 10, give superior noise suppression but fail to preserve the image’s structural and fine details at higher noise levels. The ED of the CT2 image at gaussian noise level 10, 20 gives better outcomes. In the experimental results of,13<\/sup> as shown in Fig. 11, the suppression of noise is performed well. If noise variance has increased, the resulting image overall looks blurry. The experimental results of the proposed technique as depicted in Fig. 12, illustrate that the proposed study mitigates noise effectively and also retain edges, other structural, and fine details of an image. The experimental outcomes are tested on different noisy intensities; however, the images are displayed only at noise variance 10. <\/p>\n\n\n\n

The proposed algorithm combines\nNSST with a thresholding function and its noise-based CNN approach. This\napproach exploits NSST with Bayes thresholding to get denoised NSST\ncoefficients. Here, the NSST domain  provides various  features of an image depicts in different\ndimensions and different directional subbands. The main benefit of recommended\nmethodology is, applying the method noise-based CNN approach gives better noise\nreduction and preserves edge\u2019s information. In high textured, noisy CT images,\nsome residuals or the image’s structural and fine details may get damaged\nduring denoising using the NSST domain. To overcome that, the proposed method\nnoise-based approach using CNN gives better performance in order to improve\nimage quality. Performance metrics like PSNR, SNR, SSIM, ED, and UIQI have\nproven that the proposed method remarkably reduces noise at different noise\nintensities and also provides better images and fine detail preservation as\ncompared to other denoising techniques. Here, the ED values in the proposed\nmethod are near zero. Hence, it has been proven this novel hybrid approach gives\nimprovised outcomes in case of visual clarity, quality, and performance\nbenchmarks.<\/p>\n\n\n\n\n\n
\"\"<\/td>\n\n

Figure 14:<\/strong> The line segment is used for intensity profile of image 1 for all denoising approaches<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
\"\"<\/td>\n\n

Figure 15:<\/strong> Intensity profiles of clean image, noisy image and proposed approach, respectively;<\/strong><\/p>\n

<\/p>\n

Click here to view Figure<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n

(a). Intensity profile of clean image against noisy image and proposed filtered image9<\/sup>; (b) Intensity profile of clean image ,noisy image and proposed filtered  image6<\/sup>; (c) Intensity profile of clean image ,noisy image and proposed filtered image7<\/sup>; (d) Intensity profile of clean image ,noisy image and proposed filtered image17<\/sup>; (e) Intensity profile of clean image ,noisy image and proposed filtered image11<\/sup>; (f) Intensity profile of clean image ,noisy image and proposed filtered image12<\/sup>; (g) Intensity profile of clean image ,noisy image and proposed filtered image13<\/sup>; (h) Intensity profile of clean image, noisy image and proposed filtered image28<\/sup>; (i) Intensity profile of clean image, noisy image and proposed filtered image.<\/p>\n\n\n\n

Another critical assessment for addressing variations among noisy CT image, clean CT image, and denoised or filtered CT image, is obtaining the pixel’s intensity\u2019s profile. The outcome shows the  clean image, a noisy image (noise variance 10), and a denoised or filtered CT image\u2019s intensity profile as shown in Fig. 14, the lowest difference has been figured out between an original or clean image and proposed denoised image i.e, the ensembled method  provides effective noise suppression as well as preserving edges and fine details.<\/p>\n\n\n\n

Conclusion and Future work<\/strong><\/p>\n\n\n\n

The CT images are extensively used in the medical and healthcare domain, as they precisely recognise the abnormality information of the patient. In the proposed work, initially  gaussian noise was added at various levels, ranging in noise variance from 5 to 20. These noise variances are used to estimate the efficacy of various denoising techniques. The proposed study includes NSST and a noise-based CNN method to remove Gaussian noise in CT images. Here, NSST is used as a preprocessing operation to resolve the noisy CT image into various frequency subbands. Bayesian thresholding is applied to denoise noisy NSST coefficients. After denoising NSST coefficients, a postprocessing approach is used to get residuals that were preserved in denoised CT images. The DnCNN was applied to method noise to extract structural information and fine details of CT images. The experimental study employed four CT scan images, i.e., CT2, CT3, and CT4. Standard denoising filters were applied to noisy CT images. All experimental outcomes in proposed method are evaluated against standard methods. So,  the ensembled method gives benchmarked performance in case of PSNR, SNR, SSIM, ED, and UIQI. The proposed study has proven that the experimental results from Table.no. from 1 to 5 and Fig.no. from  5 to 15, shows  better results over the CT imaging from the perspective of visual quality.<\/p>\n\n\n\n

For future work, must investigate the integration of advanced deep learning models to further improve denoising effectiveness and enhance computational efficiency. Moreover, broadening the study to encompass a larger and more varied collection of CT images can verify the reliability of the proposed method. Analyzing the use of the technique in various medical imaging modalities such as X-rays or MRI or could expand its applicability. Implementing real-time denoising features would improve clinical practices. Finally, analyzing the effect of denoising on diagnostic precision and patient outcomes would reveal valuable insights and understanding of its practical value.<\/p>\n\n\n\n

Acknowledgment<\/strong><\/p>\n\n\n\n

I\nwould like to express my deepest gratitude to my PhD supervisor, Prof. Deepak\nGarg, for his invaluable guidance, support, and encouragement throughout the\ncourse of this research. His insightful feedback and unwavering mentorship have\nbeen instrumental in shaping this work. I am equally grateful to my\nco-supervisor, Dr. Prabhishek Singh, for his constant advice, suggestions, and\nsupport, which have been crucial in navigating the complex challenges of this research\nwork. A special thanks to Prof. Manoj Diwakar for sharing his expert knowledge\nand providing specific insights on CT image denoising, which significantly\ncontributed to the refinement and depth of this research.<\/p>\n\n\n\n

Funding Sources<\/strong><\/p>\n\n\n\n

The\nauthor(s) received no financial support for the research, authorship, and\/or\npublication of this article.\n<\/p>\n\n\n\n

Conflict of Interest<\/strong><\/p>\n\n\n\n

The authors\ndo not have any conflict of interest<\/p>\n\n\n\n

References<\/strong><\/p>\n\n\n\n

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     CrossRef <\/a><\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"

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