Dictionary learning for Poisson compressed sensing

Imaging techniques involve counting of photons striking a detector. Due to fluctuations in the counting process, the measured photon counts are known to be corrupted by Poisson noise. In this paper, we propose a blind dictionary learning framework for the reconstruction of photographic image data from Poisson corrupted measurements acquired by a compressive camera. We exploit the inherent non-negativity of the data by modeling the dictionary as well as the sparse dictionary coefficients as non-negative entities, and infer these directly from the compressed measurements in a Poisson maximum likelihood framework. We experimentally demonstrate the advantage of this in situ dictionary learning over commonly used sparsifying bases such as DCT or wavelets, especially on color images.