R-FUSE: Robust Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation

TL;DR

This paper introduces a robust and efficient multi-band image fusion method that improves upon previous approaches by reducing computational cost and increasing robustness through an innovative use of the Woodbury formula and avoiding certain assumptions.

Contribution

The paper presents a novel algorithm that solves the Sylvester matrix equation more robustly and efficiently, eliminating the need for permutation operations and kernel invertibility assumptions.

Findings

More robust fusion compared to previous methods

Reduced computational complexity

Effective with various priors

Abstract

This paper proposes a robust fast multi-band image fusion method to merge a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. Following the method recently developed in [1], the generalized Sylvester matrix equation associated with the multi-band image fusion problem is solved in a more robust and efficient way by exploiting the Woodbury formula, avoiding any permutation operation in the frequency domain as well as the blurring kernel invertibility assumption required in [1]. Thanks to this improvement, the proposed algorithm requires fewer computational operations and is also more robust with respect to the blurring kernel compared with the one in [1]. The proposed new algorithm is tested with different priors considered in [1]. Our conclusion is that the proposed fusion algorithm is more robust than the one in [1] with a reduced computational cost.