Convergence Analysis for a Primal-Dual Monotone + Skew Splitting Algorithm with Applications to Total Variation Minimization

The total variation-based Rudin–Osher–Fatemi model is an effective and popular prior model in the image processing problem. Different to frequently using the splitting scheme to directly solve this model, we propose the primal dual method to solve the smoothing total variation-based Rudin–Osher–Fatemi model and give some convergence analysis of proposed method. Numerical implements show that our proposed model and method can efficiently improve the numerical results compared with the Rudin–Osher–Fatemi model.

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Total Variation Based Parameter-Free Model for Impulse Noise Removal

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2017.m1613 ◽

2017 ◽

Vol 10 (1) ◽

pp. 186-204 ◽

Cited By ~ 1

Author(s):

Federica Sciacchitano ◽

Yiqiu Dong ◽

Martin S. Andersen

Keyword(s):

Total Variation ◽

Impulse Noise ◽

Regularization Parameter ◽

Noise Removal ◽

Phase Method ◽

Second Phase ◽

Dual Algorithm ◽

Two Phase ◽

Total Variation Minimization ◽

Primal Dual

AbstractWe propose a new two-phase method for reconstruction of blurred images corrupted by impulse noise. In the first phase, we use a noise detector to identify the pixels that are contaminated by noise, and then, in the second phase, we reconstruct the noisy pixels by solving an equality constrained total variation minimization problem that preserves the exact values of the noise-free pixels. For images that are only corrupted by impulse noise (i.e., not blurred) we apply the semismooth Newton's method to a reduced problem, and if the images are also blurred, we solve the equality constrained reconstruction problem using a first-order primal-dual algorithm. The proposed model improves the computational efficiency (in the denoising case) and has the advantage of being regularization parameter-free. Our numerical results suggest that the method is competitive in terms of its restoration capabilities with respect to the other two-phase methods.

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The convergence of a numerical method for total variation flow

Journal of Algorithms & Computational Technology ◽

10.1177/17483026211011323 ◽

2021 ◽

Vol 15 ◽

pp. 174830262110113

Author(s):

Qianying Hong ◽

Ming-jun Lai ◽

Jingyue Wang

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Numerical Method ◽

Convergence Analysis ◽

Total Variation ◽

Iterative Algorithm ◽

Finite Difference Scheme ◽

Gradient Flow ◽

Time Dependent ◽

Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

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