EM-TV methods for inverse problems with poisson noise

Alex Sawatzky, Christoph Brune, Thomas Kösters, Frank Wübbeling, Martin Burger

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

27 Citations (Scopus)

Abstract

We address the task of reconstructing images corrupted by Poisson noise, which is important in various applications such as fluorescence microscopy (Dey et al., 3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization, 2004), positron emission tomography (PET; Vardi et al., J Am Stat Assoc 80:8-20, 1985), or astronomical imaging (Lantéri and Theys, EURASIP J Appl Signal Processing 15:2500-2513, 2005). Here 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 (Dey et al., 3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization, 2004; Jonsson et al., Total variation regularization in positron emission tomography, 1998; Panin et al., IEEE Trans Nucl Sci 46(6):2202-2210, 1999). However, most of these 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 lecture is to provide accurate, robust and fast EM-TV based methods for computing cartoon reconstructions facilitating post-segmentation and providing a basis for quantification techniques. We illustrate also the performance of the proposed algorithms and confirm the analytical concepts by 2D and 3D synthetic and real-world results in optical nanoscopy and PET.

Original languageEnglish
Title of host publicationLevel Set and PDE Based Reconstruction Methods in Imaging
Subtitle of host publicationCetraro, Italy 2008, Editors: Martin Burger, Stanley Osher
PublisherSpringer Verlag
Pages71-142
Number of pages72
ISBN (Electronic)978-3-319-01712-9
ISBN (Print)978-3-319-01711-2
DOIs
Publication statusPublished - 2013
Externally publishedYes

Publication series

NameLecture Notes in Mathematics
Volume2090
ISSN (Print)0075-8434

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  • Cite this

    Sawatzky, A., Brune, C., Kösters, T., Wübbeling, F., & Burger, M. (2013). EM-TV methods for inverse problems with poisson noise. In Level Set and PDE Based Reconstruction Methods in Imaging: Cetraro, Italy 2008, Editors: Martin Burger, Stanley Osher (pp. 71-142). (Lecture Notes in Mathematics; Vol. 2090). Springer Verlag. https://doi.org/10.1007/978-3-319-01712-9_2