Conformal and Low-Rank Sparse Representation for Image Restoration

Obtaining an appropriate dictionary is the key point when sparse representation is applied to computer vision or image processing problems such as image restoration. It is expected that preserving data structure during sparse coding and dictionary learning can enhance the recovery performance. However, many existing dictionary learning methods handle training samples individually, while missing relationships between samples, which result in dictionaries with redundant atoms but poor representation ability. In this paper, we propose a novel sparse representation approach called conformal and low-rank sparse representation (CLRSR) for image restoration problems. To achieve a more compact and representative dictionary, conformal property is introduced by preserving the angles of local geometry formed by neighboring samples in the feature space. Furthermore, imposing low-rank constraint on the coefficient matrix can lead more faithful subspaces and capture the global structure of data. We apply our CLRSR model to several image restoration tasks to demonstrate the effectiveness.