  The problem of Poisson denoising appears in various imaging applications,
such as low-light photography, medical imaging and microscopy. In cases of high
SNR, several transformations exist so as to convert the Poisson noise into an
additive i.i.d. Gaussian noise, for which many effective algorithms are
available. However, in a low SNR regime, these transformations are
significantly less accurate, and a strategy that relies directly on the true
noise statistics is required. A recent work by Salmon et al. took this route,
proposing a patch-based exponential image representation model based on GMM
(Gaussian mixture model), leading to state-of-the-art results. In this paper,
we propose to harness sparse-representation modeling to the image patches,
adopting the same exponential idea. Our scheme uses a greedy pursuit with
boot-strapping based stopping condition and dictionary learning within the
denoising process. The reconstruction performance of the proposed scheme is
competitive with leading methods in high SNR, and achieving state-of-the-art
results in cases of low SNR.
