Image restoration via the adaptive TVp regularization

Pang, Zhi-Feng and Meng, Ge and Li, Hui and Chen, Ke (2020) Image restoration via the adaptive TVp regularization. Computers and Mathematics with Applications, 80 (5). pp. 569-587. ISSN 0898-1221 (https://doi.org/10.1016/j.camwa.2020.04.030)

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Abstract

To keep structures in the restoration problem is very important via coupling the local information of the image with the proposed model. In this paper we propose a local self-adaptive ℓp -regularization model for p ∈ (0, 2) based on the total variation scheme, where the choice of p depends on the local structures described by the eigenvalues of the structure tensor. Since the proposed model as the classic ℓp problem unifies two classes of optimization problems such as the nonconvex and nonsmooth problem when p ∈ (0, 1), and the convex and smooth problem when p ∈ (1, 2), it is generally challenging to find a ready algorithmic framework to solve it. Here we propose a new and robust numerical method via coupling with the half-quadratic scheme and the alternating direction method of multipliers (ADMM). The convergence of the proposed algorithm is established and the numerical experiments illustrate the possible advantages of the proposed model and numerical methods over some existing variational-based models and methods.

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