Hyperspectral Super-resolution: A Coupled Nonnegative Block-term Tensor Decomposition Approach

Hyperspectral super-resolution (HSR) aims at fusing a hyperspectral image (HSI) and a multispectral image (MSI) to produce a super-resolution image (SRI). Recently, a coupled tensor factorization approach was proposed to handle this challenging problem, which admits a series of advantages over the classic matrix factorization-based methods. In particular, modeling the HSI and MSI as low-rank tensors following the {\it canonical polyadic decomposition} (CPD) model, the approach is able to provably identify the SRI, under some mild conditions. However, the latent factors in the CPD model have no physical meaning, which makes utilizing prior information of spectral images as constraints or regularizations difficult---but using such information is often important in practice, especially when the data is noisy. In this work, we propose an alternative coupled tensor decomposition approach, where the HSI and MSI are assumed to follow the {\it block-term decomposition (BTD)} model. Notably, the new method also entails identifiability of the SRI under realistic conditions. More importantly, when modeling a spectral image as a BTD tensor, the latent factors have clear physical meaning, and thus prior knowledge about spectral images can be naturally incorporated. Simulations using real hyperspectral images are employed to showcase the effectiveness of the proposed approach with nonnegativity constraints.Comment: This paper was accepted by IEEE CAMSAP on Sep.17, 201

Is There Any Recovery Guarantee with Coupled Structured Matrix Factorization for Hyperspectral Super-Resolution?

Coupled structured matrix factorization (CoSMF) for hyperspectral super-resolution (HSR) has recently drawn significant interest in hyperspectral imaging for remote sensing. Presently there is very few work that studies the theoretical recovery guarantees of CoSMF. This paper makes one such endeavor by considering the CoSMF formulation by Wei et al., which, simply speaking, is similar to coupled non-negative matrix factorization. Assuming no noise, we show sufficient conditions under which the globably optimal solution to the CoSMF problem is guaranteed to deliver certain recovery accuracies. Our analysis suggests that sparsity and the pure-pixel (or separability) condition play a hidden role in enabling CoSMF to achieve some good recovery characteristics.Comment: submitted to CAMSAP 2019, extended versio