Constrainted Subspace Low-Rank Representation with Spatial-Spectral Total Variation for Hyperspectral Image Restoration

Abstract

The restoration of hyperspectral Images (HSIs) corrupted by mixed noise is an important preprocessing step. In an HSI cube, the spectral vectors can be separated into different classification based on the land-covers, which means the spectral space can be regarded as an union of several low-rank subspaces. Subspace low-rank representation (SLRR) is a powerful tool in exploring the inner low-rank structure of spectral space and has been applied for HSI restoration. However, the traditional SLRR framework only seek for the rank-minimum representation under a given dictionary, which may treat the structured sparse noise as inherent low-rank components. In addition, the SLRR framework cannot make full use of the spatial information. In this paper, a framework named constrainted subspace low-rank representation with spatial-spectral total variation (CSLRR-SSTV) is proposed for HSI restoration. In which, an artificial rank constraint is involved into the SLRR framework to control the rank of the representation result, which can improve the removal of the structured sparse noise and exploit the intrinsic structure of spectral space more effectively, and the SSTV regularization is applied to enhance the spatial and spectral smoothness. Several experiments conducted in simulated and real HSI datasets demonstrate that the proposed method can achieve a state-of-the-art performance both in visual quality and quantitative assessments.