Blind deconvolution using bilateral total variation regularization: a theoretical study and application

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.

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Super-resolution image reconstruction based on Tukey data fusion and bilateral-total-variation regularization

Optical Review ◽

10.1007/s10043-014-0006-0 ◽

2014 ◽

Vol 21 (1) ◽

pp. 35-42

Author(s):

Yan Chen ◽

Shuhua Wang ◽

Weiqi Jin ◽

Guangping Wang ◽

Weili Chen ◽

...

Keyword(s):

Image Reconstruction ◽

Data Fusion ◽

Total Variation ◽

Super Resolution ◽

Total Variation Regularization ◽

Resolution Image ◽

Bilateral Total Variation

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Nonlocal Low-Rank Regularization Combined with Bilateral Total Variation for Compressive Sensing Image Reconstruction

Electronics ◽

10.3390/electronics10040385 ◽

2021 ◽

Vol 10 (4) ◽

pp. 385

Author(s):

Kunhao Zhang ◽

Yali Qin ◽

Huan Zheng ◽

Hongliang Ren ◽

Yingtian Hu

Keyword(s):

Image Reconstruction ◽

Compressive Sensing ◽

Total Variation ◽

Sampling Rate ◽

Low Rank ◽

Reconstructed Image ◽

Total Variation Regularization ◽

Edge Information ◽

Reconstruction Performance ◽

Bilateral Total Variation

The use of non-local self-similarity prior between image blocks can improve image reconstruction performance significantly. We propose a compressive sensing image reconstruction algorithm that combines bilateral total variation and nonlocal low-rank regularization to overcome over-smoothing and degradation of edge information which result from the prior reconstructed image. The proposed algorithm makes use of the preservation of image edge information by bilateral total variation operator to enhance the edge details of the reconstructed image. In addition, we use weighted nuclear norm regularization as a low-rank constraint for similar blocks of the image. To solve this convex optimization problem, the Alternating Direction Method of Multipliers (ADMM) is employed to optimize and iterate the algorithm model effectively. Experimental results show that the proposed algorithm can obtain better image reconstruction quality than conventional algorithms with using total variation regularization or considering the nonlocal structure of the image only. At 10% sampling rate, the peak signal-to-noise ratio gain is up to 2.39 dB in noiseless measurements compared with Nonlocal Low-rank Regularization (NLR-CS). Reconstructed image comparison shows that the proposed algorithm retains more high frequency components. In noisy measurements, the proposed algorithm is robust to noise and the reconstructed image retains more detail information.

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Edge-preserving total variation regularization for dual-energy CT images

Electronic Imaging ◽

10.2352/issn.2470-1173.2019.13.coimg-147 ◽

2019 ◽

Vol 2019 (13) ◽

pp. 147-1-147-8

Author(s):

Sandamali Devadithya ◽

David Castañóon

Keyword(s):

Total Variation ◽

Ct Images ◽

Dual Energy ◽

Dual Energy Ct ◽

Total Variation Regularization ◽

Edge Preserving

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

Remote Sensing ◽

10.3390/rs13132514 ◽

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.

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