Hyperspectral Image Restoration via Subspace-Based Nonlocal Low-Rank Tensor Approximation

Abstract

In this letter, we present a subspace-based nonlocal low-rank tensor approximation framework (SNLRTA) for hyperspectral image (HSI) restoration. The proposed method consists of a subspace learning method to achieve an accurate subspace characterization of HSI and a nonlocal low-rank tensor approximation to take spatial nonlocal self-similarity into consideration. Specifically, the HSI first exploits residual statistics on median filtered image to estimate a robust subspace. Laplacian scale mixture (LSM) modeling is then investigated to model tensor coefficients from overlapping cubes in low-rank subspace. Both the hidden scale parameters and the sparse coefficients therein are adaptively shrink, characterizing the sparsity of similar patches. Meanwhile, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> data fidelity facilitates the implicit detection of outliers after median filtering. Substantiated by extensive experimental results, the proposed method outperforms several state-of-the-art approaches on mixed noise removal, qualitatively and quantitatively.