scholarly journals Total Variation Regularization Algorithms for Images Corrupted with Different Noise Models: A Review

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Paul Rodríguez
Keyword(s):  
Total Variation ◽  
Blind Deconvolution ◽  
Numerical Algorithms ◽  
Total Variation Regularization ◽  
General Technique ◽  
Denoising Method ◽  
Tv Regularization ◽  
Mixed Noise ◽  
Map Estimator ◽  
Noise Models

Total Variation (TV) regularization has evolved from an image denoising method for images corrupted with Gaussian noise into a more general technique for inverse problems such as deblurring, blind deconvolution, and inpainting, which also encompasses the Impulse, Poisson, Speckle, and mixed noise models. This paper focuses on giving a summary of the most relevant TV numerical algorithms for solving the restoration problem for grayscale/color images corrupted with several noise models, that is, Gaussian, Salt & Pepper, Poisson, and Speckle (Gamma) noise models as well as for the mixed noise scenarios, such the mixed Gaussian and impulse model. We also include the description of the maximum a posteriori (MAP) estimator for each model as well as a summary of general optimization procedures that are typically used to solve the TV problem.

scholarly journals An Improved Particle Swarm Optimization Based on Total Variation Regularization and Projection Constraint with Applications in Ground-Penetrating Radar Inversion: A Model Simulation Study

2021 ◽  
Vol 13 (13) ◽  
pp. 2514
Author(s):  
Qianwei Dai ◽  
Hao Zhang ◽  
Bin Zhang
Keyword(s):  
Particle Swarm Optimization ◽  
Total Variation ◽  
Ground Penetrating Radar ◽  
Particle Swarm ◽  
Premature Convergence ◽  
Total Variation Regularization ◽  
Interface Model ◽  
Swarm Optimization ◽  
Tv Regularization ◽  
Ground Penetrating

The chaos oscillation particle swarm optimization (COPSO) algorithm is prone to binge trapped in the local optima when dealing with certain complex models in ground-penetrating radar (GPR) data inversion, because it inherently suffers from premature convergence, high computational costs, and extremely slow convergence times, especially in the middle and later periods of iterative inversion. Considering that the bilateral connections between different particle positions can improve both the algorithmic searching efficiency and the convergence performance, we first develop a fast single-trace-based approach to construct an initial model for 2-D PSO inversion and then propose a TV-regularization-based improved PSO (TVIPSO) algorithm that employs total variation (TV) regularization as a constraint technique to adaptively update the positions of particles. B by adding the new velocity variations and optimal step size matrices, the search range of the random particles in the solution space can be significantly reduced, meaning blindness in the search process can be avoided. By introducing constraint-oriented regularization to allow the optimization search to move out of the inaccurate region, the premature convergence and blurring problems can be mitigated to further guarantee the inversion accuracy and efficiency. We report on three inversion experiments involving multilayered, fluctuated terrain models and a typical complicated inner-interface model to demonstrate the performance of the proposed algorithm. The results of the fluctuated terrain model show that compared with the COPSO algorithm, the fitness error (MAE) of the TVIPSO algorithm is reduced from 2.3715 to 1.0921, while for the complicated inner-interface model the fitness error (MARE) of the TVIPSO algorithm is reduced from 1.9539 to 1.5674.

scholarly journals Image Compression Approach using Segmentation and Total Variation Regularization

2021 ◽  
Vol 15 ◽  
pp. 43-47
Author(s):  
Ahmad Shahin ◽  
Walid Moudani ◽  
Fadi Chakik
Keyword(s):  
Image Compression ◽  
Total Variation ◽  
Image Data ◽  
Smart Devices ◽  
Multimedia Content ◽  
Total Variation Regularization ◽  
Second Stage ◽  
Tv Regularization ◽  
Rof Model

In this paper we present a hybrid model for image compression based on segmentation and total variation regularization. The main motivation behind our approach is to offer decode image with immediate access to objects/features of interest. We are targeting high quality decoded image in order to be useful on smart devices, for analysis purpose, as well as for multimedia content-based description standards. The image is approximated as a set of uniform regions: The technique will assign well-defined members to homogenous regions in order to achieve image segmentation. The Adaptive fuzzy c-means (AFcM) is a guide to cluster image data. A second stage coding is applied using entropy coding to remove the whole image entropy redundancy. In the decompression phase, the reverse process is applied in which the decoded image suffers from missing details due to the coarse segmentation. For this reason, we suggest the application of total variation (TV) regularization, such as the Rudin-Osher-Fatemi (ROF) model, to enhance the quality of the coded image. Our experimental results had shown that ROF may increase the PSNR and hence offer better quality for a set of benchmark grayscale images.

In vivo blind-deconvolution photoacoustic ophthalmoscopy with total variation regularization

2018 ◽  
Vol 11 (9) ◽  
pp. e201700360 ◽  
Author(s):  
Deyan Xie ◽  
Qin Li ◽  
Quanxue Gao ◽  
Wei Song ◽  
Hao F. Zhang ◽  
...  
Keyword(s):  
Total Variation ◽  
Blind Deconvolution ◽  
Total Variation Regularization

scholarly journals TV2++: A Novel Spatial-Temporal Total Variation for Super Resolution with Exponential-type Norm

2020 ◽  
Author(s):  
Lizhen Deng ◽  
Zhetao Zhou ◽  
Guoxia Xu ◽  
Hu Zhu ◽  
Bing-Kun Bao
Keyword(s):  
Total Variation ◽  
Exponential Type ◽  
Optimization Problems ◽  
Super Resolution ◽  
Low Rank ◽  
Good Effect ◽  
Total Variation Regularization ◽  
Time Dimension ◽  
Tv Regularization ◽  
Image Super Resolution

Abstract Recently, many super-resolution algorithms have been proposed to recover high resolution images to improve visualization and help better analyze images. Among them, total variation regularization (TV) methods have been proven to have a good effect in retaining image edge information. However, these TV methods do not consider the temporal correlation between images. Our algorithm designs a new TV regularization (TV2++) to take advantage of the time dimension information of the images, further improving the utilization of useful information in the images. In addition, the union of global low rank regularization and TV regularization further enhances the image super resolution recovery. And we extend the exponential-type penalty (ETP) function on singular values of a matrix to enhance low-rank matrix recovery. A novel image super-resolution algorithm based on the ETP norm and TV2++ regularization is proposed. And the alternating direction method of multipliers (ADMM) is applied to solve the optimization problems effectively. Numerous experimental results prove that the proposed algorithm is superior to other algorithms.

scholarly journals TV2++: A Novel Spatial-Temporal Total Variation for Super Resolution with Exponential-type Norm

2020 ◽  
Author(s):  
Lizhen Deng ◽  
Zhetao Zhou ◽  
Guoxia Xu ◽  
Hu Zhu ◽  
Bing-Kun Bao
Keyword(s):  
Total Variation ◽  
Exponential Type ◽  
Optimization Problems ◽  
Super Resolution ◽  
Low Rank ◽  
Good Effect ◽  
Total Variation Regularization ◽  
Time Dimension ◽  
Tv Regularization ◽  
Image Super Resolution

Abstract Recently, many super-resolution algorithms have been proposed to recover high resolution images to improve visualization and help better analyze images. Among them, total variation regularization (TV) methods have been proven to have a good effect in retaining image edge information. However, these TV methods do not consider the temporal correlation between images. Our algorithm designs a new TV regularization (TV2++) to take advantage of the time dimension information of the images, further improving the utilization of useful information in the images. In addition, the union of global low rank regularization and TV regularization further enhances the image super resolution recovery. And we extend the exponential-type penalty (ETP) function on singular values of a matrix to enhance low-rank matrix recovery. A novel image super-resolution algorithm based on the ETP norm and TV2++ regularization is proposed. And the alternating direction method of multipliers (ADMM) is applied to solve the optimization problems effectively. Numerous experimental results prove that the proposed algorithm is superior to other algorithms.

Total variation regularization for depth-to-basement estimate: Part 2 — Physicogeologic meaning and comparisons with previous inversion methods

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. I13-I20 ◽  
Author(s):  
Williams A. Lima ◽  
Cristiano M. Martins ◽  
João B. Silva ◽  
Valeria C. Barbosa
Keyword(s):  
Total Variation ◽  
Regularization Parameter ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Total Variation Regularization ◽  
Discontinuous Solutions ◽  
Mathematical Basis ◽  
Inversion Methods ◽  
Tv Regularization ◽  
Entropic Regularization

We applied the mathematical basis of the total variation (TV) regularization to analyze the physicogeologic meaning of the TV method and compared it with previous gravity inversion methods (weighted smoothness and entropic Regularization) to estimate discontinuous basements. In the second part, we analyze the physicogeologic meaning of the TV method and compare it with previous gravity inversion methods (weighted smoothness and entropic regularization) to estimate discontinuous basements. Presenting a mathematical review of these methods, we show that minimizing the TV stabilizing function favors discontinuous solutions because a smooth solution, to honor the data, must oscillate, and the presence of these oscillations increases the value of the TV stabilizing function. These three methods are applied to synthetic data produced by a simulated 2D graben bordered by step faults. TV regularization and weighted smoothness are also applied to the real anomaly of Steptoe Valley, Nevada, U.S.A. In all applications, the three methods perform similarly. TV regularization, however, has the advantage, compared with weighted smoothness, of requiring no a priori information about the maximum depth of the basin. As compared with entropic regularization, TV regularization is much simpler to use because it requires, in general, the tuning of just one regularization parameter.

scholarly journals TV2++: a novel spatial-temporal total variation for super resolution with exponential-type norm

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lizhen Deng ◽  
Zhetao Zhou ◽  
Guoxia Xu ◽  
Hu Zhu ◽  
Bing-Kun Bao
Keyword(s):  
Total Variation ◽  
Exponential Type ◽  
Optimization Problems ◽  
Super Resolution ◽  
Low Rank ◽  
Good Effect ◽  
Total Variation Regularization ◽  
Time Dimension ◽  
Tv Regularization ◽  
Image Super Resolution

Abstract Recently, many super-resolution algorithms have been proposed to recover high-resolution images to improve visualization and help better analyze images. Among them, total variation regularization (TV) methods have been proven to have a good effect in retaining image edge information. However, these TV methods do not consider the temporal correlation between images. Our algorithm designs a new TV regularization (TV2++) to take advantage of the time dimension information of the images, further improving the utilization of useful information in the images. In addition, the union of global low rank regularization and TV regularization further enhances the image super-resolution recovery. And we extend the exponential-type penalty (ETP) function on singular values of a matrix to enhance low-rank matrix recovery. A novel image super-resolution algorithm based on the ETP norm and TV2++ regularization is proposed. And the alternating direction method of multipliers (ADMM) is applied to solve the optimization problems effectively. Numerous experimental results prove that the proposed algorithm is superior to other algorithms.

scholarly journals Collocation Method for Multiplicative Noise Removal Model

2020 ◽  
Vol 39 (4) ◽  
pp. 734-743
Author(s):  
Mushtaq Ahmad Khan ◽  
Zawar Hussain Khan ◽  
Haseeb khan ◽  
Sheraz Khan ◽  
Suhail Khan
Keyword(s):  
Image Denoising ◽  
Multiplicative Noise ◽  
Fundamental Problem ◽  
Lagrange Equation ◽  
Noise Removal ◽  
Original Image ◽  
General Technique ◽  
Denoising Method ◽  
Tv Regularization ◽  
Multiplicative Noise Removal

Image denoising is a fundamental problem in both image processing and computer vision with numerous applications. It can be formulated as an inverse problem. Variational methods are commonly used to solve noise removal problems. The Total Variation (TV) regularization has evolved from an image denoising method for images corrupted with multiplicative noise into a more general technique for inverse problems such as denoising, deblurring, blind deconvolution, and inpainting, which also encompasses the Impulse, Poisson, Speckle, and mixed noise models. Multiplicative noise removal based on TV regularization has been widely researched in image science. In multiplicative noise problems, original image is multiplied by a noise rather than added to the original image. This article proposes a novel meshless collocation technique for the solution of a model having multiplicative noise. This technique includes TV and local collocation along with Multiquadric Radial Basis Function (MQ-RBF) for the solution of associated Euler-Lagrange equation for restoring multiplicative noise from digital images. Numerical examples demonstrate that the proposed algorithm is able to preserve small image details while the noise in the homogeneous regions is removed sufficiently. As a consequence, our method yields better denoised results than those of the current state of the art methods with respect to the Peak-Signal to Noise Ratio (PSNR) values.

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