A Generalized Tensor Formulation for Hyperspectral Image Super-Resolution Under General Spatial Blurring

TL;DR

This paper introduces a generalized tensor-based method for hyperspectral image super-resolution that effectively models complex, anisotropic spatial blurring, leading to improved image reconstruction over existing separable models.

Contribution

It proposes a Kronecker-based tensor formulation that handles non-separable spatial degradation, extending the modeling capabilities beyond traditional assumptions.

Findings

Outperforms traditional matrix-based super-resolution methods.

Significantly improves results in cases of anisotropic blurring.

Provides theoretical conditions for exact image recovery.

Abstract

Hyperspectral super-resolution is commonly accomplished by the fusing of a hyperspectral imaging of low spatial resolution with a multispectral image of high spatial resolution, and many tensor-based approaches to this task have been recently proposed. Yet, it is assumed in such tensor-based methods that the spatial-blurring operation that creates the observed hyperspectral image from the desired super-resolved image is separable into independent horizontal and vertical blurring. Recent work has argued that such separable spatial degradation is ill-equipped to model the operation of real sensors which may exhibit, for example, anisotropic blurring. To accommodate this fact, a generalized tensor formulation based on a Kronecker decomposition is proposed to handle any general spatial-degradation matrix, including those that are not separable as previously assumed. Analysis of the generalized formulation reveals conditions under which exact recovery of the desired super-resolved image is guaranteed, and a practical algorithm for such recovery, driven by a blockwise-group-sparsity regularization, is proposed. Extensive experimental results demonstrate that the proposed generalized tensor approach outperforms not only traditional matrix-based techniques but also state-of-the-art tensor-based methods; the gains with respect to the latter are especially significant in cases of anisotropic spatial blurring.