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

Abstract EN

Recovering a large matrix from limited measurements is a challenging task arisingin many real applications, such as image inpainting, compressive sensing, andmedical imaging, and these kinds of problems are mostly formulated as low-rankmatrix approximation problems.

Due to the rank operator being nonconvexand discontinuous, most of the recent theoretical studies use the nuclear normas a convex relaxation and the low-rank matrix recovery problem is solvedthrough minimization of the nuclear norm regularized problem.

However, amajor limitation of nuclear norm minimization is that all the singular valuesare simultaneously minimized and the rank may not be well approximated (Hu et al., 2013).

Correspondingly, in this paper, we propose a new multistage algorithm, whichmakes use of the concept of Truncated Nuclear Norm Regularization (TNNR)proposed by Hu et al., 2013, and iterative support detection (ISD) proposed by Wang and Yin, 2010, to overcomethe above limitation.

Besides matrix completion problems considered by Hu et al., 2013, the proposed method can be also extended to the general low-rank matrixrecovery problems.

Extensive experiments well validate the superiority of ournew algorithms over other state-of-the-art methods.