Nonconvex TVq model with l1</sub? fidelity term in image restoration

Lampayan, Valentine Blez L.; Neri, Marrick C.

VOLUME 17 NUMBER 1 (January to June 2024)

PSL%202021 vol14-no01-p12-28-Mikita%20and%20Padlan

SciEnggJ. 2024 17 (1) 018-026
available online: January 22, 2024
DOI: https://doi.org/10.54645/2024171MXS-35

*Corresponding author
Email Address: mcneri@up.edu.ph
Date received: April 20, 2023
Date revised: November 20, 2023
Date accepted: December 19, 2023

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ARTICLE

Nonconvex TV_q model with l1 fidelity term in image restoration

Valentine Blez L. Lampayan and Marrick C. Neri*

Institute of Mathematics, University of the Philippines-Diliman,
Quezon City, 1101 Philippines

KEYWORDS: nonconvex total variation, image processing, active set method

Restoration of images based on a nonconvex l₁ variational model which contains the l_q “norm,” q ∈ (0,1), is considered. The existence of a minimizer of the model is established in the discrete setting. To solve the minimization problem, Huber-type regularizations of the l_q and the l₁norms are performed on the model. A primal-dual semismooth Newton method with a trust region technique is adapted to solve the model and the convergence of the algorithm is presented. Applications are made on restoration of images corrupted with blur and impulse noise.