Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Topic-based language models using Dirichlet Mixtures
Systems and Computers in Japan
Pairwise likelihood estimation for multivariate mixed Poisson models generated by Gamma intensities
Statistics and Computing
Wavelet-based statistical signal processing using hidden Markovmodels
IEEE Transactions on Signal Processing
Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging
IEEE Transactions on Information Theory
A statistical multiscale framework for Poisson inverse problems
IEEE Transactions on Information Theory
Wavelet-domain filtering for photon imaging systems
IEEE Transactions on Image Processing
Discrete Markov image modeling and inference on the quadtree
IEEE Transactions on Image Processing
Bayesian tree-structured image modeling using wavelet-domain hidden Markov models
IEEE Transactions on Image Processing
The curvelet transform for image denoising
IEEE Transactions on Image Processing
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
Improved Poisson intensity estimation: denoising application using Poisson data
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal
IEEE Transactions on Image Processing
Poisson-Haar transform: a nonlinear multiscale representation for photon-limited image denoising
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Wavelet-Based De-noising of Positron Emission Tomography Scans
Journal of Scientific Computing
Poisson image denoising using geometric platelets and geometric quadlets
Signal Processing
Simplified noise model parameter estimation for signal-dependent noise
Signal Processing
A New Poisson Noise Filter Based on Weights Optimization
Journal of Scientific Computing
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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.