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 the existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms. Index Terms-Multi-band image fusion, Bayesian estimation, circulant matrix, Sylvester equation, alternating direction method of multipliers, block coordinate descent.
Wei et al. REF have proposed an efficient Bayesian model, in which maximizing the likelihood corresponds to solving a Sylvester equation.
Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Mathematics Medicine Computer Science