Proximal linearized alternating direction method of multipliers algorithm for nonconvex image restoration with impulse noise

• Published in: IET image processing Vol. 17; no. 14; pp. 4044 - 4060
• Main Authors: Tang, Yuchao, Deng, Shirong, Peng, Jigen, Zeng, Tieyong
• Format: Journal Article
• Language: English
• Published: Wiley 01.12.2023
• Subjects: image denoising; impulse noise
• ISSN: 1751-9659; 1751-9667
• DOI: 10.1049/ipr2.12917

Image restoration with impulse noise is an important task in image processing. Taking into account the statistical distribution of impulse noise, the ℓ1‐norm data fidelity and total variation (ℓ1TV$\ell _1TV$) model has been widely used in this area. However, the ℓ1TV$\ell _1TV$ model usually performs worse when the noise level is high. To overcome this drawback, several nonconvex models have been proposed. In this paper, an efficient iterative algorithm is proposed to solve nonconvex models arising in impulse noise. Compared to existing algorithms, the proposed algorithm is a completely explicit algorithm in which every subproblem has a closed‐form solution. The key idea is to transform the original nonconvex models into an equivalent constrained minimization problem with two separable objective functions, where one is differentiable but nonconvex. As a consequence, the proximal linearized alternating direction method of multipliers is employed to solve it. Extensive numerical experiments are presented to demonstrate the efficiency and effectiveness of the proposed algorithm. We propose a fully splitting algorithm based on the proximal linearized alternating direction method of multipliers for nonconvex models for image restoration with impulse noise. We show how many specific nonconvex impulse noise models can be solved by our algorithm. We conduct extensive numerical experiments to compare the efficiency and effectiveness of our algorithm with other popular methods.