Fusion of Hyperspectral and Multispectral Images Based on a Bayesian Nonparametric Approach

This paper presents a new approach to fusion of hyperspectral and multispectral images based on Bayesian nonparametric sparse representation. The approach formulates the image fusion problem within a constrained optimization framework, while assuming that the target image lives in a lower dimensional subspace. The subspace transform matrix is determined by principal component analysis, and the sparse regularization term is designed depending on a set of dictionaries and sparse coefficients associated with the observed images. Specifically, the dictionary elements and sparse coefficients are learned by the Bayesian nonparametric approach with the beta-Bernoulli process, which establishes the probability distribution models for each latent variable and calculates the posterior distributions by Gibbs sampling. Finally, serving the obtained posterior distributions as a priori, the fusion problem is solved via an alternate optimization process, where the alternate direction method of multipliers is applied to perform the optimization with respect to the target image. The Bayesian nonparametric method is used to optimize the sparse coefficients. Exhaustive experiments using both two public datasets and one real-world dataset of remote sensing images show that the proposed approach outperforms the existing state-of-the-art methods.