SLRQA: A Sparse Low-Rank Quaternion Model for Color Image Processing with Convergence Analysis
Authors
Zhanwang Deng, Yuqiu Su, and Wen Huang*
Abstract
In this paper, we propose a Sparse Low-rank Quaternion Approximation (SLRQA) model for color image processing problems with noisy observations. The proposed SLRQA is a quaternion model that combines low-rankness and sparsity priors. Furthermore, it does not need an initial rank estimate. To solve the SLRQA model, a nonconvex proximal linearized ADMM (PLADMM) algorithm is proposed. Furthermore, the global convergence analysis of the PL-ADMM under mild assumptions is presented. When the observation is noise-free, an SLRQA-NF model of the limiting case of the SLRQA is proposed. Subsequently, a nonconvex proximal linearized ADMM (PL-ADMM-NF) algorithm for the SLRQA-NF is given. In numerical experiments, we verify the effectiveness of quaternion representation. Furthermore, for color image denoising and color image inpainting problems, SLRQA and SLRQA-NF models demonstrate superior performance both quantitatively and visually when compared with some state-of-the-art methods.
Key words
Color image denoising, Quaternion matrix completion, Nonconvex linearized ADMM
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