A novel multi-scale LRMR method for hyperspectral images restoration

Simultaneously recovering hyperspectral images (HSIs) from mixed degradations is a classical inverse problem, which has attracted major research efforts. Low-rank matrix recovery (LRMR) has been proved to be an effective method. This paper proposes a multi-scale recovering model based on 3D Gaussian pyramid decomposition and residual reconstitution to improve the LRMR on its adaptability of local correlative noises (including stripes, dead lines and impulse noise) removal. By compressing the HSI cube to lower-resolution layers in spatial domain, the non-local low rank property of clean HSI can be better utilized. LRMR algorithm is applied from the top. The following layers are reconstituted with the upper recovery result and their original decomposition residual, and then executed LRMR until the bottom of the pyramid. In the proposed procedure, mixed noises are removed progressively in terms of frequency, besides the details of clean HSI are well preserved. Experimental results on simulated and real data in terms of qualitative and quantitative assessments show significant improvements over conventional methods.