Poisson-Haar Transform: A nonlinear multiscale representation for photon-limited image denoising

We present a novel multiscale image representation belonging to the class of multiscale multiplicative decompositions, which we term Poisson-Haar transform. The proposed representation is well-suited for analyzing images degraded by signal-dependent Poisson noise, allowing efficient estimation of their underlying intensity by means of multiscale Bayesian schemes. The Poisson-Haar decomposition has a direct link to the standard 2D Haar wavelet transform, thus retaining many of the properties that have made wavelets successful in signal processing and analysis. The practical relevance and effectiveness of the proposed approach is verified through denoising experiments on simulated and real-world photon-limited images.