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Forward-Backward EM-TV methods for inverse problems with Poisson noise
| Citations: | 5 - 3 self |
BibTeX
@MISC{Brune_forward-backwardem-tv,
author = {Christoph Brune and Martin Burger and Alex Sawatzky},
title = {Forward-Backward EM-TV methods for inverse problems with Poisson noise},
year = {}
}
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Abstract
Abstract. We address the task of reconstructing images corrupted by Poisson noise, which is important in various applications, such as fluorescence microscopy, positron emission tomography (PET), or astronomical imaging. In this work, we focus on reconstruction strategies, combining the expectation-maximization (EM) algorithm and total variation (TV) based regularization, and present a detailed analysis as well as numerical results. Recently extensions of the well known EM/Richardson-Lucy algorithm received increasing attention for inverse problems with Poisson data. However, most algorithms for regularizations like TV lead to convergence problems for large regularization parameters, cannot guarantee positivity, and rely on additional approximations (like smoothed TV). The goal of this work is to provide an accurate, robust and fast FB-EM-TV method for computing cartoon reconstructions facilitating post-segmentation and further image quantifications. Motivated by several applications we provide a statistical modeling of inverse problems with Poisson noise in terms of Bayesian
Keyphrases
inverse problem poisson noise forward-backward em-tv method several application numerical result image quantification cartoon reconstruction additional approximation astronomical imaging total variation positron emission tomography recently extension poisson data em richardson-lucy algorithm cannot guarantee positivity statistical modeling various application fast fb-em-tv method large regularization parameter reconstruction strategy detailed analysis fluorescence microscopy tv lead
