{Pan-sharpening with a Bayesian nonparametric dictionary learning model}

Pan-sharpening, a method for constructing high resolution images from low resolution obser-vations, has recently been explored from the perspective of compressed sensing and sparse representation theory. We present a new pan-sharpening algorithm that uses a Bayesian non-parametric dictionary learning model to give an underlying sparse representation for image re-construction. In contrast to existing dictionary learning methods, the proposed method infers parameters such as dictionary size, patch spar-sity and noise variances. In addition, our reg-ularization includes image constraints such as a total variation penalization term and a new gra-dient penalization on the reconstructed PAN im-age. Our method does not require high resolution multiband images for dictionary learning, which are unavailable in practice, but rather the dictio-nary is learned directly on the reconstructed im-age as part of the inversion process. We present experiments on several images to validate our method and compare with several other well-known approaches. 1