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.