Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising

Abstract

Abstract-We present an improved statistical model for analyzing 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 contributions include: 1) a rigorous and robust regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of the rate-ratio density parameters directly from the noisy observed Poisson data (counts); 2) extension of the method to work under a multiscale hidden Markov tree model (HMT) which couples the mixture label assignments in consecutive scales, thus modeling interscale coefficient dependencies in the vicinity of image edges; 3) exploration of a 2-D recursive quad-tree image representation, involving Dirichlet-mixture rate-ratio densities, instead of the conventional separable binary-tree image representation involving beta-mixture rate-ratio densities; and 4) a novel multiscale image representation, which we term Poisson-Haar decomposition, that better models the image edge structure, thus yielding improved performance. Experimental results on standard images with artificially simulated Poisson noise and on real photon-limited images demonstrate the effectiveness of the proposed techniques.

A Survey of Multispectral Image Denoising Methods for Satellite Imagery Applications

“…Thus, in the well-illuminated environment, the source of noise introduction is the random arrival of photons and the AWGN noise dominated the deterioration of the actual signal. However, in a setting involves with the poor lighting environment, the significant amount of noise introduction to the actual signal is contributed by the stochastic nature of the signal itself, where a mixed Poisson-Gaussian distribution of noise model is taken in account upon which several denoising algorithms had been built [30,31]. There are also other approaches which apply suitable transformations to reduce the problem of regular AWGN noise [32].…”

Undecimated haar thresholding for poisson intensity estimation

“…We have compared our algorithm with three state-of-the-art methods in simulated experiments: the Anscombe VST [1] followed by the BLS-GSM denoiser applied in a full steerable pyramid [3], the Platelet approach exposed in [8] and the Poisson-Haar hidden Markov tree (PH-HMT) introduced in [7]. The near shift-invariance of these last two algorithms is achieved by averaging the denoising results obtained on several shifted versions of the input image (cycle-spinning strategy).…”

“…* The second is the direct handling of Poisson statistics often in a Bayesian [5][6][7] or in a penalized likelihood [8] framework. Statistical priors or penalty terms are commonly formulated in a multiscale decomposition, where the Poisson intensities are sparsely represented.…”

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

“…For this class of methods we use as VSTs the Anscombe [8] and Haar-Fisz [9] transforms and as denoising method the popular wavelet-domain SureShrink [10] employing Daubechies wavelets of 5 vanishing moments. For more extensive comparisons one can also refer to [11] where an extension of this work is presented. The quality of the resulting images is measured in terms of peak SNR (PSNR).…”