Hyperspectral Image Mixed Noise Removal via Nonlinear Transform-Based Block-Term Tensor Decomposition

Abstract

Recently, block-term decomposition with rank-( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_r</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_r</i> ,1) (termed as LL1 decomposition), which is physically inspired by linear spectral unmixing, has received increasing attention in hyperspectral images (HSIs) denoising. However, due to the intrinsic nonlinear structure of real-world HSIs, the low-rankness of HSIs is usually implicit. Moreover, the essential uniqueness guarantee is usually violated with the low-rank assumption of the abundance maps unsupported in real scenarios, which hampers the successful deployment of LL1 decomposition. Inspired by the nonlinear spectral unmixing, we propose a nonlinear learnable transform-based LL1 decomposition (NT-LL1) for characterizing the implicit low-rank structure of real-world HSIs. More concretely, the nonlinear learnable transform in NT-LL1 decomposition is a composed transform consisting of a linear semi-orthogonal transform and a component-wise nonlinear transform, which collaboratively enhances the low-rankness of the abundance maps. Empowering with the NT-LL1 decomposition, we propose an NT-LL1 decomposition-based model for HSIs denoising. To tackle the resulting model, we develop an efficient proximal alternating minimization-based algorithm with a convergence guarantee. Extensive experimental results including simulated and real data collectively verify the superiority of the proposed method as compared with the competing methods.