Truncated Nuclear Norm Minimization for Image Restoration Based On Iterative Support Detection

TL;DR

This paper introduces a multi-stage algorithm combining Truncated Nuclear Norm Regularization and Iterative Support Detection to improve low-rank matrix recovery, especially in image restoration tasks, outperforming existing methods.

Contribution

The paper proposes a novel multi-stage algorithm that integrates TNNR and ISD to better approximate matrix rank in low-rank recovery problems.

Findings

The proposed method outperforms state-of-the-art algorithms in image restoration.

Extensive experiments validate the effectiveness of the new approach.

The algorithm extends to general low-rank matrix recovery beyond matrix completion.

Abstract

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation and the low-rank matrix recovery problem is solved through minimization of the nuclear norm regularized problem. However, a major limitation of nuclear norm minimization is that all the singular values are simultaneously minimized and the rank may not be well approximated \cite{hu2012fast}. Correspondingly, in this paper, we propose a new multi-stage algorithm, which makes use of the concept of Truncated Nuclear Norm Regularization (TNNR) proposed in \citep{hu2012fast} and Iterative Support Detection (ISD) proposed in \citep{wang2010sparse} to overcome the above limitation. Besides matrix completion problems considered in \citep{hu2012fast}, the proposed method can be also extended to the general low-rank matrix recovery problems. Extensive experiments well validate the superiority of our new algorithms over other state-of-the-art methods.