Photon-limited image denoising by inference on multiscale models
We present an improved statistical model of Poisson processes, with applications to photon-limited imaging. We build on previous work, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities (rates) in adjacent scales are modeled as mixtures of conjugate parametric distributions. Our main novel contributions are (1) a rigorous and robust regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of the rate-ratio density parameters directly from the observed Poisson data (counts); (2) extension of the method to work under a scale-recursive hidden Markov tree model (HMT) which couples the mixture label assignments in consecutive scales, thus modeling inter-scale coefficient dependencies in the vicinity of edges; and (3) exploration of a fully 2-D quad-tree image partitioning, involving Dirichlet-mixture rate-ratio densities, instead of the conventional separable binary image partitioning involving Beta-mixture rate-ratio densities. Experimental intensity estimation results on standard images with artificially simulated Poisson noise and photon-limited images with real shot noise demonstrate the effectiveness of the proposed approach.