Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation

TL;DR

This paper introduces a fast multi-band image fusion method that efficiently combines images with different spatial and spectral resolutions by solving a Sylvester equation explicitly, reducing computational complexity.

Contribution

The paper presents a novel closed-form solution for the Sylvester equation in multi-band image fusion, enabling faster computation without iterative updates.

Findings

Achieves similar performance to existing methods

Significantly reduces computational complexity

Easily incorporates prior information for Bayesian fusion

Abstract

This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods of the observations. Maximizing the likelihoods leads to solving a Sylvester equation. By exploiting the properties of the circulant and downsampling matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained explicitly, getting rid of any iterative update step. Coupled with the alternating direction method of multipliers and the block coordinate descent method, the proposed algorithm can be easily generalized to incorporate prior information for the fusion problem, allowing a Bayesian estimator. Simulation results show that the proposed algorithm achieves the same performance as existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms.