Application In Image Denoising Research Articles

Convex set-oriented singular value decomposition with bounded uncertainties

Singular value decomposition (SVD) has played a crucial role in mathematics and applied mathematics, particularly in the field of practical engineering technology, which is almost indispensable in these fields. However, incomplete information caused by uncertainties from multiple sources and fluctuations in inherent properties during engineering practice can seriously interfere with obtaining singular values. Based on the convex set uncertainty theory, a novel convex set-oriented singular value decomposition (CSSVD) is proposed to overcome the limitations of using the nominal SVD method. The CSSVD aims to accurately and efficiently calculate the uncertainty bounds of singular values and vectors through the bounds and correlations of initial uncertainty parameters. Traditional probability methods rely on a sufficient sample size, and when the sample size is insufficient, accurate results cannot be obtained. However, the CSSVD method is based on set theory and can still demonstrate excellent performance in scenarios with small samples. This study investigates the detailed derivation steps of the proposed CSSVD method, taking into consideration properties such as normalization, orthogonality, and Monte Carlo simulation (MCS) to verify the accurate bounds of convex sets. The proposed method is finally applied to several numerical examples to demonstrate its superiority. This includes verifying singular values and vectors, handling high-order matrices, matrices with close singular values, and rectangular matrices. An application of image denoising is also used to evaluate the effectiveness of the proposed method.

The use of physics-informed neural network approach to image restoration via nonlinear PDE tools

In this work, we propose a physics-informed solution for a blending PDE model with application in image denoising and edge-preserving. The blending model contains isotropic diffusion (ID) model and the modified Perona-Malik model introduced by Catte et al. Then we solve this model applying a physics-informed approach. Solving the new blending model is done using DeepXDE, which is a deep learning library for solving differential equations, by considering the image as input. Error analysis for neural network approximations of the new PDE model is shown. Applying PSNR criteria for some images, it can be seen that the proposed method can compete with solving denoising PDE models using finite difference method (FDM).

Fractional Calculus in Signal Processing: The Use of Fractional Calculus in Signal Processing Applications, Such as Image Denoising, Filtering, and Time Series Analysis

Fractional calculus has transformed signal processing by providing a more flexible representation of complex signals. This article explores its applications in image denoising, filtering, and time series analysis, highlighting its potential to revolutionize signal processing methodologies. Fractional calculus, dealing with derivatives and integrals of non-integer orders, captures long-memory and self-similar properties in real-world signals. Image denoising benefits from fractional derivatives and integrals, preserving essential details while removing noise. Filtering signals with fractional calculus allows for dynamic adaptability to changing signal characteristics. Time series analysis benefits from more accurate modelling, enhancing predictive capabilities. The future scope of fractional calculus in signal processing promises further advancements, making it a valuable tool for researchers and practitioners seeking to analyze complex signals across various domains.

TextureWGAN: texture preserving WGAN with multitask regularizer for computed tomography inverse problems.

This paper presents a deep learning (DL) based method called TextureWGAN. It is designed to preserve image texture while maintaining high pixel fidelity for computed tomography (CT) inverse problems. Over-smoothed images by postprocessing algorithms have been a well-known problem in the medical imaging industry. Therefore, our method tries to solve the over-smoothing problem without compromising pixel fidelity. The TextureWGAN extends from Wasserstein GAN (WGAN). The WGAN can create an image that looks like a genuine image. This aspect of the WGAN helps preserve image texture. However, an output image from the WGAN is not correlated to the corresponding ground truth image. To solve this problem, we introduce the multitask regularizer (MTR) to the WGAN framework to make a generated image highly correlated to the corresponding ground truth image so that the TextureWGAN can achieve high-level pixel fidelity. The MTR is capable of using multiple objective functions. In this research, we adopt a mean squared error (MSE) loss to maintain pixel fidelity. We also use a perception loss to improve the look and feel of result images. Furthermore, the regularization parameters in the MTR are trained along with generator network weights to maximize the performance of the TextureWGAN generator. The proposed method was evaluated in CT image reconstruction applications in addition to super-resolution and image-denoising applications. We conducted extensive qualitative and quantitative evaluations. We used PSNR and SSIM for pixel fidelity analysis and the first-order and the second-order statistical texture analysis for image texture. The results show that the TextureWGAN is more effective in preserving image texture compared with other well-known methods such as the conventional CNN and nonlocal mean filter (NLM). In addition, we demonstrate that TextureWGAN can achieve competitive pixel fidelity performance compared with CNN and NLM. The CNN with MSE loss can attain high-level pixel fidelity, but it often damages image texture. TextureWGAN can preserve image texture while maintaining pixel fidelity. The MTR is not only helpful to stabilize the TextureWGAN's generator training but also maximizes the generator performance.

Local Adaptiveness of Mixed Higher Order Partial Differential Equations and Its Application in Image Denoising

Background: Image denoising methods based on partial differential equations have attracted much attention due to their "infinite" local adaptation capabilities, high flexibility, and strong mathematical theoretical support. Methods: This paper proposes a mixed higher order partial differential equation denoising model for the step effect caused by the second-order denoising model and the edge blur caused by the fourth-order denoising model. The model combines the second-order and fourth-order terms based on the relationship between the variational energy minimization and the partial differential equations. The fourth-order term is used to remove noise in the uniform area of the image to avoid the step effect, and the second-order term is used at the edge to avoid boundary blur. Results: Theoretical analysis and numerical experiment results show that the proposed model has weak solutions and can effectively avoid the step effect and maintain the edge. Conclusion: The image denoising results of the model are better than those of other improved denoising models in subjective effect, and objective evaluation indicators, such as SNR, PSNR, and MSSIM.

A Skewness Fitting Model for Noise Level Estimation and the Applications in Image Denoising

In this paper, a novel noise level estimation technique is presented based on skewness fitting. The difference between exact skewness and observed value on each channel contributes to an objective function. The skewness concentration is helpful to guarantee the reasonability of the model. The optimal solution means an estimation of the noise variance and it is easy to be applied in some parametric denoising model. The accuracy and efficiency of proposed algorithm were verified by the numerical experiments.

Noise Intensity Estimation Method Based on PCA and Weak Textured Block Selection for Neutron Image

Noise intensity estimation has a very important application in image denoising. In image processing, the denoising method can achieve an ideal denoising effect under the assumption that the Gaussian noise intensity in the image is known. But in real denoising applications, especially the neutron image, the noise level is unknown, which will greatly affect the denoising effect of neutron image processing. In this paper, a method which combined the principal component analysis with weak texture block selection is proposed for noise intensity estimation of neutron images. The experimental results show that the proposed method can accurately estimate the Gaussian noise in the neutron image. Compared with the existing noise intensity estimation methods, the qualitative and quantitative results show that the proposed method has higher accuracy and stability.

Deep-learning denoising computational ghost imaging

We propose a deep learning denoising computational ghost imaging (CGI) method to obtain a clear object image with a sub-Nyquist sampling ratio. We develop an end-to-end deep neural network (DDANet) for CGI image reconstruction. DDANet uses a one-dimensional (1-D) bucket signals (BSs) and multiple tunable noise-level maps as input, and outputs a clear image. We train DDANet with simulated BSs and ground-truth pairs, and then retrieve the object image directly from an experimental obtained 1-D BSs. The effectiveness of the proposed method is experimentally investigated. The proposed method has practical applications in image denoising and enhancement of the CGI and single-pixel computational imaging.

Adaptive Deep Cascade Broad Learning System and Its Application in Image Denoising

This article proposes a novel regularization deep cascade broad learning system (DCBLS) architecture, which includes one cascaded feature mapping nodes layer and one cascaded enhancement nodes layer. Then, the transformation feature representation is easily obtained by incorporating the enhancement nodes and the feature mapping nodes. Once such a representation is established, a final output layer is constructed by implementing a simple convex optimization model. Furthermore, a parallelization framework on the new method is designed to make it compatible with large-scale data. Simultaneously, an adaptive regularization parameter criterion is adopted under some conditions. Moreover, the stability and error estimate of this method are discussed and proved mathematically. The proposed method could extract sufficient available information from the raw data compared with the standard broad learning system and could achieve compellent successes in image denoising. The experiments results on benchmark datasets, including natural images as well as hyperspectral images, verify the effectiveness and superiority of the proposed method in comparison with the state-of-the-art approaches for image denoising.

Wavelet-Based Self-adaptive Hierarchical Thresholding Algorithm and Its Application in Image Denoising

Wavelet-Based Self-adaptive Hierarchical Thresholding Algorithm and Its Application in Image Denoising

Geometrical X-lets for Image Denoising.

There has been a lot of researches allocated to image denoising in recent years. One of the appropriate approaches for image denoising is applying nonlinear thresholding techniques in time-frequency transform domains. These transforms decompose an image to a series of elementary waveforms called basis functions or dictionary atoms. Different directional time-frequency dictionaries provide various geometrical X-let transforms in two or higher dimensions. In this paper, we have a comparative study of geometrical X-let transforms including 2D-Discrete Wavelet (2D-DWT), Dual-Tree Complex Wavelet (DT-CWT), Curvelet, Contourlet, Steerable Pyramid (STP) and Circlet Transform (CT) in application of image denoising. Experimental results show that in synthetic images of Optical Coherence Tomography (OCT), the Steerable Pyramid outperforms other geometrical X-lets in terms of Peak Signal-to-Noise Ratio (PSNR), while DT-CWT is superior in terms of Structural Similarity Index (SSIM). Moreover, in real images of OCT which consist of retinal layers, Curvelet Transform has better results in terms of Contrast-to-Noise Ratio (CNR) and 2D-DWT is better in Edge Preservation (EP) and Texture Preservation (TP) which indicate various X-lets can be effective due to different criteria and different images.

Piecewise Linear Regression Based on Plane Clustering

Piecewise linear regressions have shown many successful applications in image denoising, signal process, and data mining fields. In essence, they attempt to seek multiple linear functions (piecewise/stepwise function) to fit the given scatter data points by various methodologies, typically point-centered clustering methods, such as ${k}$ -means or fuzzy c means. Obviously, it is reasonable that plane-centered clustering is more suitable for capturing the linearities in data. In this paper, we propose an efficient piecewise linear regression method based on ${k}$ -plane clustering, termed as PlrPC. The proposed method first partitions the data into multiple plane-centered clusters and then analytically compute corresponding piecewise linear functions. Compared with the state-to-the-art linear regressors, the advantages of the PlrPC lie in fourfold: 1) it is generated from plane clustering, which is truly coincident with geometrical intuition; 2) to fuse the linear characteristics into plane clustering, a new implicit regression method is proposed; 3) a new plane jump method is proposed to detect the number of clusters, and; 4) the leading problem can be solved by ordinary eigenvalue problems. The experimental results will show the aforesaid characters on some artificial and some benchmark datasets.

Dilated residual encode–decode networks for image denoising

Owing to recent advancements, very deep convolutional neural networks (CNNs) have found application in image denoising. However, while deeper models lead to better restoration performance, they are marred by a high number of parameters and increased training difficulty. To address these issues, we propose a CNN-based framework, named dilated residual encode–decode networks (DRED-Net), for image denoising, which learns direct end-to-end mappings from corrupted images to obtain clean images using few parameters. Our proposed network consists of multiple layers of convolution and deconvolution operators; in addition, we use dilated convolutions to boost the performance of our network without increasing the depth of the model or its complexity. Extensive experiments on synthetic noisy images are conducted to evaluate DRED-Net, and the results are compared with those obtained using state-of-the-art denoising methods. Our experimental results show that DRED-Net leads to results comparable with those obtained using other state-of-the-art methods for image denoising tasks.

An Improved Method on Non-subsampled Contourlet Transform Ultrasonic Image Denoising

The non-subsampled contourlet transform (NSCT) is a good approach in capturing the detail of images, so that it has a wide range of applications in image denoising. In order to improve the denoising effect of NSCT method of medical ultrasound images, the local intuitionistic fuzzy entropy (LIFE) theory is employed in this work to suppress the noise in the high-frequency coefficients of NSCT. On combination with the LIFE theory and the directionality of the coefficients’ distribution of NSCT, the directional local intuitionistic fuzzy entropy (DLIFE) method has been put forward to calculate the corresponding noise suppression factor to remove the noise in the high-frequency coefficients of NSCT. The experiments on both Barbara image and medical ultrasound image show a better denoising effect than the original NSCT soft threshold method and the wavelet soft threshold method.

Quantum image median filtering in the spatial domain

Spatial filtering is one principal tool used in image processing for a broad spectrum of applications. Median filtering has become a prominent representation of spatial filtering because its performance in noise reduction is excellent. Although filtering of quantum images in the frequency domain has been described in the literature, and there is a one-to-one correspondence between linear spatial filters and filters in the frequency domain, median filtering is a nonlinear process that cannot be achieved in the frequency domain. We therefore investigated the spatial filtering of quantum image, focusing on the design method of the quantum median filter and applications in image de-noising. To this end, first, we presented the quantum circuits for three basic modules (i.e., Cycle Shift, Comparator, and Swap), and then, we design two composite modules (i.e., Sort and Median Calculation). We next constructed a complete quantum circuit that implements the median filtering task and present the results of several simulation experiments on some grayscale images with different noise patterns. Although experimental results show that the proposed scheme has almost the same noise suppression capacity as its classical counterpart, the complexity analysis shows that the proposed scheme can reduce the computational complexity of the classical median filter from the exponential function of image size n to the second-order polynomial function of image size n, so that the classical method can be speeded up.

Quantum Image Weighted Average Filtering in Spatial Domain

In this paper, we investigated the quantum image spatial filtering, and focused on the design method of quantum weighted averaging filter and its application in image de-noising. To this end, we first designed the quantum circuits for some auxiliary modules, such as swapping two numbers, comparing two numbers, computing the weighted average of some integers, etc. Next, we constructed a weighted averaging filter of size 3 × 3 using auxiliary modules. The spatial filtering directly on the image itself can be accomplished by using designed filter. We provided the quantum circuits that implements the filtering task and presented the results of several simulation experiments on some gray images with different noises. The significance of this paper is to explore the quantum realization method of image filtering in spatial domain.

Optimizing Shrinkage Curves and Application in Image Denoising

A shrinkage curve optimization is proposed for weighted nuclear norm minimization and is adapted to image denoising. The proposed optimization method employs a penalty function utilizing the difference between a latent matrix and its observation and uses odd polynomials to shrink the singular values of the observation matrix. As a result, the coefficients of polynomial characterize the shrinkage operator fully. Furthermore, the Frobenius norm of the penalty function is converted into the corresponding spectral norm, and thus the parameter optimization problem can be easily solved by using off-and-shelf plain least-squares. In the practical application, the proposed denoising method does not work on the whole image at once, but rather a series of matrix termed Rank-Ordered Similar Matrix (ROSM). Simulation results on 256 noisy images demonstrate the effectiveness of the proposed algorithms.

Noise Estimation for Images using Eigen Values and Frobenius norm

Performance of image denoising algorithm is critically dependent on the accuracy of noise level estimation. In the estimation process, restricting the influence of image content on the estimation dataset is a major challenge. In this paper, we propose a novel method which involves the application of Frobenius norm as the basis of content energy measurement. It involves the truncation of SVD (Singular Value Decomposition) components thereby effectively restricting the influence of image details. Application of linear regression for determining content parameter enhances the application scope of the proposed method. The experimental results demonstrates the effectiveness of the proposed approach. Keywords—Frobenius norm, noise estimation, singular value decomposition, linear regression, additive white gaussian noise I. INTRODUCTION Application of Image Denoising or Filtering algorithms is desirable for images corrupted with additive white gaussian noise. This step is applied before many processing algorithms such as image segmentation, restoration etc. Many of these filtering or denoising algorithms rely on the information about the incurred level of noise which is assumed to be known apriori. In real-time applications, this information is obtained by estimation techniques. Accuracy and reliability of estimation algorithms thus affects the filtering or denoising processes concomitantly. More often the noise is assumed to be zero mean additive white gaussian in nature (3), whose distribution is characterized by following equation:

Statistics of Natural Stochastic Textures and Their Application in Image Denoising.

Natural stochastic textures (NSTs), characterized by their fine details, are prone to corruption by artifacts, introduced during the image acquisition process by the combined effect of blur and noise. While many successful algorithms exist for image restoration and enhancement, the restoration of natural textures and textured images based on suitable statistical models has yet to be further improved. We examine the statistical properties of NST using three image databases. We show that the Gaussian distribution is suitable for many NST, while other natural textures can be properly represented by a model that separates the image into two layers; one of these layers contains the structural elements of smooth areas and edges, while the other contains the statistically Gaussian textural details. Based on these statistical properties, an algorithm for the denoising of natural images containing NST is proposed, using patch-based fractional Brownian motion model and regularization by means of anisotropic diffusion. It is illustrated that this algorithm successfully recovers both missing textural details and structural attributes that characterize natural images. The algorithm is compared with classical as well as the state-of-the-art denoising algorithms.

Compressed Sensing Method Application in Image Denoising

In order to improve the work of a single path network reliability failure case, this chapter put forward a set of a single backup path algorithm based on the path. In this algorithm, using two disjoint paths as work path to transmit data, and USES the path does not intersect with the job of a set the path as the backup path. Then, this algorithm, is proposed based on a single - a single backup path algorithm of shortest path set to ensure data under the case of the second work path of effective transmission. Theoretical derivation and numerical simulation results show that in a single work path failure cases, and the calculation of DMP - compared to BP algorithm, this scheme can greatly improve network reliability, and save the network resources.