EM-TV methods for inverse problems with poisson noise

Beitrag in einem Sammelwerk


Details zur Publikation

Autorinnen und Autoren: Sawatzky A, Brune C, Kösters T, Wübbeling F, Burger M
Herausgeber: Burger Martin, Osher Stanley
Titel Sammelwerk: Level Set and PDE-based Reconstruction Methods
Verlag: Springer
Jahr der Veröffentlichung: 2013
Titel der Reihe: Lecture Notes in Mathematics
Seitenbereich: 71-142
ISBN: 9783319017112
ISSN: 0075-8434
Sprache: Englisch


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.


Einrichtungen weiterer Autorinnen und Autoren

University of California Los Angeles (UCLA)
Westfälische Wilhelms-Universität (WWU) Münster


Zitierweisen

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: 

Zuletzt aktualisiert 2018-29-11 um 16:23