Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.5.2021.3.05

Volume 5, Issue 3, 1 June 2021, Pages 403-420

 

Abstract. Cartoon-texture image decomposition, which refers to the problem of decomposing an image into a cartoon part and a texture component, is one of the most fundamental problems in image processing. In this paper, we are concerned with the low patch-rank enhanced image decomposition model, which is a convex but nonsmooth optimization problem that could not be solved directly by traditional gradient-based optimization algorithms. Accordingly, we introduce two unconstrained reformulations to the underlying low patch-rank optimization model. Furthermore, by exploiting favorable structures of the resulting reformations, we propose two easily implementable alternating minimization algorithms, whose subproblems have closed-form solutions. Compared to the state-of-the-art multi-block alternating direction method of multipliers and its variants, our proposed algorithms enjoy simpler iterative schemes and lower memory requirements for saving computing time. A series of numerical experiments further support the promising performance of the proposed approaches.

 

How to Cite this Article:
Lulu Zhao, Cheng Chen, Tingxia Lu, Zhiyuan Zhang, Hongjin He, Low patch-rank image decomposition using alternating minimization algorithms, J. Nonlinear Var. Anal. 5 (2021), 403-420.