Bayesian inference on multiscale models for poisson intensity estimation: Applications to photon-limited image denoising

Lefkimmiatis, S; Maragos, P; Papandreou, G

dc.contributor.author	Lefkimmiatis, S	en
dc.contributor.author	Maragos, P	en
dc.contributor.author	Papandreou, G	en
dc.date.accessioned	2014-03-01T01:29:54Z
dc.date.available	2014-03-01T01:29:54Z
dc.date.issued	2009	en
dc.identifier.issn	1057-7149	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19400
dc.subject	Bayesian inference	en
dc.subject	Expectation-maximization (EM) algorithm	en
dc.subject	Hidden Markov tree (HMT)	en
dc.subject	Photon-limited imaging	en
dc.subject	Poisson processes	en
dc.subject	Poisson-Haar decomposition	en
dc.subject.classification	Computer Science, Artificial Intelligence	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.other	Bayesian inference	en
dc.subject.other	Expectation-maximization (EM) algorithm	en
dc.subject.other	Hidden Markov tree (HMT)	en
dc.subject.other	Photon-limited imaging	en
dc.subject.other	Poisson processes	en
dc.subject.other	Poisson-Haar decomposition	en
dc.subject.other	Bayesian networks	en
dc.subject.other	Decomposition	en
dc.subject.other	Edge detection	en
dc.subject.other	Hidden Markov models	en
dc.subject.other	Image segmentation	en
dc.subject.other	Inference engines	en
dc.subject.other	Labels	en
dc.subject.other	Maximum likelihood estimation	en
dc.subject.other	Maximum principle	en
dc.subject.other	Mixtures	en
dc.subject.other	Optimization	en
dc.subject.other	Photons	en
dc.subject.other	Poisson equation	en
dc.subject.other	Poisson distribution	en
dc.subject.other	Algorithms	en
dc.subject.other	Image Analysis	en
dc.subject.other	Mathematical Analysis	en
dc.subject.other	Optimization	en
dc.subject.other	algorithm	en
dc.subject.other	article	en
dc.subject.other	Bayes theorem	en
dc.subject.other	image processing	en
dc.subject.other	methodology	en
dc.subject.other	optics	en
dc.subject.other	Poisson distribution	en
dc.subject.other	probability	en
dc.subject.other	statistical model	en
dc.subject.other	Algorithms	en
dc.subject.other	Bayes Theorem	en
dc.subject.other	Image Processing, Computer-Assisted	en
dc.subject.other	Markov Chains	en
dc.subject.other	Models, Statistical	en
dc.subject.other	Optics and Photonics	en
dc.subject.other	Poisson Distribution	en
dc.title	Bayesian inference on multiscale models for poisson intensity estimation: Applications to photon-limited image denoising	en
heal.type	journalArticle	en
heal.identifier.primary	10.1109/TIP.2009.2022008	en
heal.identifier.secondary	http://dx.doi.org/10.1109/TIP.2009.2022008	en
heal.language	English	en
heal.publicationDate	2009	en
heal.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. © 2009 IEEE.	en
heal.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC	en
heal.journalName	IEEE Transactions on Image Processing	en
dc.identifier.doi	10.1109/TIP.2009.2022008	en
dc.identifier.isi	ISI:000268033300004	en
dc.identifier.volume	18	en
dc.identifier.issue	8	en
dc.identifier.spage	1724	en
dc.identifier.epage	1741	en