Hyperspectral Image Restoration Using Weighted Group Sparsity-Regularized Low-Rank Tensor Decomposition

• Published in: IEEE transactions on cybernetics Vol. 50; no. 8; pp. 3556 - 3570
• Main Authors: Chen, Yong, He, Wei, Yokoya, Naoto, Huang, Ting-Zhu
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Augmented Lagrange multiplier (ALM) algorithm; Computer simulation; Correlation; Decomposition; group sparsity; hyperspectral image restoration; Hyperspectral imaging; Image quality; Image restoration; Lagrange multiplier; low-rank tensor decomposition; Mathematical analysis; Matrix decomposition; Noise measurement; Regularization; Sparsity; Spectra; Spectral bands; Spectral correlation; Tensors
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2019.2936042

Mixed noise (such as Gaussian, impulse, stripe, and deadline noises) contamination is a common phenomenon in hyperspectral imagery (HSI), greatly degrading visual quality and affecting subsequent processing accuracy. By encoding sparse prior to the spatial or spectral difference images, total variation (TV) regularization is an efficient tool for removing the noises. However, the previous TV term cannot maintain the shared group sparsity pattern of the spatial difference images of different spectral bands. To address this issue, this article proposes a group sparsity regularization of the spatial difference images for HSI restoration. Instead of using <inline-formula> <tex-math notation="LaTeX">\ell _{1} </tex-math></inline-formula>- or <inline-formula> <tex-math notation="LaTeX">\ell _{2} </tex-math></inline-formula>-norm (sparsity) on the difference image itself, we introduce a weighted <inline-formula> <tex-math notation="LaTeX">\ell _{2,1} </tex-math></inline-formula>-norm to constrain the spatial difference image cube, efficiently exploring the shared group sparse pattern. Moreover, we employ the well-known low-rank Tucker decomposition to capture the global spatial-spectral correlation from three HSI dimensions. To summarize, a weighted group sparsity-regularized low-rank tensor decomposition (LRTDGS) method is presented for HSI restoration. An efficient augmented Lagrange multiplier algorithm is employed to solve the LRTDGS model. The superiority of this method for HSI restoration is demonstrated by a series of experimental results from both simulated and real data, as compared with the other state-of-the-art TV-regularized low-rank matrix/tensor decomposition methods.