Logarithmic total variation regularization for cross-validation in photon-limited imaging

In fields such as astronomy and medicine, many imaging modalities operate in the photon-limited realm because of the low photon counts available over a reasonable exposure time. Photon-limited observations are often modeled as the composite of a linear operator, such as a blur or tomographic projection, applied to a scene of interest, followed by Poisson noise draws for each pixel. One method to reconstruct the underlying scene intensity is to minimize a regularized Poisson negative log-likelihood, but choosing a good scaling parameter for the regularizer is notoriously difficult. This paper presents a new model that solves for and regularizes the logarithm of the true scene, and focuses on the special case of total variation regularization. This method yields considerable gains when used in conjunction with cross-validation for regularization parameter selection, where weighting of the regularization term is automatically determined using observed data.