Hyperspectral Image Restoration via Global <i>L<sub>1-2</sub> </i> Spatial–Spectral Total Variation Regularized Local Low-Rank Tensor Recovery
Haijin Zeng, Xiaozhen Xie, Haojie Cui, Hanping Yin, Jifeng Ning
Abstract
Hyperspectral images (HSIs) are usually corrupted by various noises, e.g., Gaussian noise, impulse noise, stripes, dead lines, and many others. In this article, motivated by the good performance of the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-2</sub> nonconvex metric in image sparse structure exploitation, we first develop a 3-D L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-2</sub> spatial-spectral total variation ( L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-2</sub> SSTV) regularization to globally represent the sparse prior in the gradient domain of HSIs. Then, we divide HSIs into local overlapping 3-D patches, and low-rank tensor recovery (LTR) is locally used to effectively separate the low-rank clean HSI patches from complex noise. The patchwise LTR can not only adapt to the local low-rank property of HSIs well but also significantly reduce the information loss caused by the global LTR. Finally, integrating the advantages of both the global L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-2</sub> SSTV regularization and local LTR model, we propose a L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-2</sub> SSTV regularized local LTR model for hyperspectral restoration. In the framework of the alternating direction method of multipliers, the difference of convex algorithm, the split Bregman iteration method, and tensor singular value decomposition method are adopted to solve the proposed model efficiently. Simulated and real HSI experiments show that the proposed model can reduce the dependence on noise independent and identical distribution hypotheses, and simultaneously remove various types of noise, even structure-related noise.