Hyperspectral image restoration by subspace representation with low-rank constraint and spatial-spectral total variation

Hyperspectral images (HSIs) restoration is an important preprocessing step. The spectral vectors in HSI can be separated into different classification based on the land-covers, which means the spectral space can be regarded as the union of several low-rank subspaces. Subspace low-rank representation (SLRR) is powerful in exploring the inner low-rank structure and has been applied for HSI restoration. However, the traditional SLRR 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 study, a framework named subspace representation with low-rank constraint and spatial-spectral total variation is proposed for HSI restoration. In which, an artificial rank constraint is introduced 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. Meanwhile, the spatial-spectral total variation regularisation 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.