EM-TV methods for inverse problems with poisson noise

Sawatzky A, Brune C, Kösters T, Wübbeling F, Burger M (2013)

Publication Language: English

Publication Type: Book chapter / Article in edited volumes

Publication year: 2013

Journal

Lecture Notes in Mathematics Springer Verlag Kg

Publisher: Springer

Edited Volumes: Level Set and PDE-based Reconstruction Methods

Series: Lecture Notes in Mathematics

Pages Range: 71-142

ISBN: 9783319017112

DOI: 10.1007/978-3-319-01712-9-2

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. © 2013 Springer International Publishing Switzerland.

Authors with CRIS profile

Martin Burger

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE) University of California Los Angeles (UCLA) US United States (USA) (US)

How to cite

APA:

Sawatzky, A., Brune, C., Kösters, T., Wübbeling, F., & Burger, M. (2013). EM-TV methods for inverse problems with poisson noise. In Burger Martin, Osher Stanley (Eds.), Level Set and PDE-based Reconstruction Methods. (pp. 71-142). Springer.

MLA:

Sawatzky, Alex, et al. "EM-TV methods for inverse problems with poisson noise." Level Set and PDE-based Reconstruction Methods. Ed. Burger Martin, Osher Stanley, Springer, 2013. 71-142.

BibTeX: Download