  In this paper, we address the problem of denoising images degraded by Poisson
noise. We propose a new patch-based approach based on best linear prediction to
estimate the underlying clean image. A simplified prediction formula is derived
for Poisson observations, which requires the covariance matrix of the
underlying clean patch. We use the assumption that similar patches in a
neighborhood share the same covariance matrix, and we use off-the-shelf Poisson
denoising methods in order to obtain an initial estimate of the covariance
matrices. Our method can be seen as a post-processing step for Poisson
denoising methods and the results show that it improves upon several Poisson
denoising methods by relevant margins.
