Bayesian dictionary learning for hyperspectral image super resolution in mixed Poisson-Gaussian noise

•We propose a beta process analysis-based sparse representation regularization term.•We learn the dictionary based on the reduced low dimension subspace.•The dictionary learning and image estimating are unified into an formulation.•We update the dictionary self-adaptively by variational Bayesian method.

This paper develops a Bayesian dictionary learning method for hyperspectral image super resolution in the presence of mixed Poisson-Gaussian noise. A likelihood function is first designed to deal with the mixed Poisson-Gaussian noise. A fusion optimization model is then introduced, including the data-fidelity term capturing the statistics of mixed Poisson-Gaussian noise, and a beta process analysis-based sparse representation regularization term. In order to implement the proposed method, we use alternating direction method of multipliers (ADMM) for simultaneous Bayesian nonparametric dictionary learning and image estimation. Compared with conventional dictionary learning methods, the introduced dictionary learning method is based on a popular beta process factor analysis (BPFA) for an adaptive learning performance. Simulation results illustrate that the proposed method has a better performance than several well-known methods in terms of quality indices and reconstruction visual effects.