ManiDec: Manifold Constrained Low-Rank and Sparse Decomposition

Abstract

Low-rank and sparse decomposition based image alignment has recently become an important research topic in the computer vision community. However, the reconstruction process often suffers from the perturbations caused by variations of the input samples. The reason behind is that the consistency of the learned low-rank and sparse structures for similar input samples is not well addressed in the existing literature. In this paper, a novel framework that embeds the manifold constraint into low-rank and sparse decomposition is proposed. Particularly, the proposed approach attempts to solve the original optimization problem directly and force the optimization process to satisfy the structure preservation requirement. Therefore, this novel manifold constrained low-rank and sparse decomposition (ManiDec) can consistently integrate the manifold constraint during the non-convex optimization process, and it can contribute a better solution which is robust to the variance of the input samples. Numerical comparisons between our proposed ManiDec and some state-of-the-art solvers, on several accessible databases, are presented to demonstrate its efficiency and effectiveness. In fact, to the best of our knowledge, this is the first time to integrate the manifold constraint into a non-convex framework, which has demonstrated the superiority of performance.

Keywords

• Low-rank and sparse decomposition
• image alignment
• manifold constraint
• non-convex optimization