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Hyperspectral Super-Resolution via Interpretable Block-Term Tensor Modeling

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Document pages: 16 pages

Abstract: This work revisits coupled tensor decomposition (CTD)-based hyperspectralsuper-resolution (HSR). HSR aims at fusing a pair of hyperspectral andmultispectral images to recover a super-resolution image (SRI). The vastmajority of the HSR approaches take a low-rank matrix recovery perspective. Thechallenge is that theoretical guarantees for recovering the SRI using low-rankmatrix models are either elusive or derived under stringent conditions. Acouple of recent CTD-based methods ensure recoverability for the SRI underrelatively mild conditions, leveraging on algebraic properties of the canonicalpolyadic decomposition (CPD) and the Tucker decomposition models, respectively.However, the latent factors of both the CPD and Tucker models have no physicalinterpretations in the context of spectral image analysis, which makesincorporating prior information challenging---but using priors is oftenessential for enhancing performance in noisy environments. This work employs anidea that models spectral images as tensors following the block-termdecomposition model with multilinear rank-$(L r, L r, 1)$ terms (i.e., the LL1model) and formulates the HSR problem as a coupled LL1 tensor decompositionproblem. Similar to the existing CTD approaches, recoverability of the SRI isshown under mild conditions. More importantly, the latent factors of the LL1model can be interpreted as the key constituents of spectral images, i.e., theendmembers spectral signatures and abundance maps. This connection allows usto easily incorporate prior information for performance enhancement. A flexiblealgorithmic framework that can work with a series of structural information isproposed to take advantage of the model interpretability. The effectiveness isshowcased using simulated and real data.

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