  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.

Computer Vision and Pattern Recognition