Coupled Tensor Models Accounting for Inter-image Variability

Abstract

Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images (respectively HSI and MSI). This problem is referred to as hyperspectral super-resolution, and consists in recovering a super-resolution image (SRI). Previously proposed tensor-based approaches share a common limitation: they assume that the observed images are acquired under exactly the same conditions. In practice, there exist very few optical satellites that carry both hyperspectral and multispectral sensors: thus, combining an HSI and an MSI acquired on board different missions has become a task of prime interest. Since the HSI and MSI are acquired at different time instants, they can differ by, e.g., illumination, atmospheric or seasonal changes. In this work, we address the problem of hyperspectral super-resolution accounting for inter-image variability. We propose a tensor degradation model accounting for variability between the observed HSI and MSI. After introducing noiseless recovery guarantees for the target SRI, we propose two algorithms based on low-rank tensor approximations. We illustrate the performance of the proposed approach for a set of synthetic and real datasets accounting for inter-image variability.