Total variation processing of images with poisson statistics

Alex Sawatzky*, Christoph Brune, Jahn Müller, Martin Burger

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

58 Citations (Scopus)


This paper deals with denoising of density images with bad Poisson statistics (low count rates), where the reconstruction of the major structures seems the only reasonable task. Obtaining the structures with sharp edges can also be a prerequisite for further processing, e.g. segmentation of objects. A variety of approaches exists in the case of Gaussian noise, but only a few in the Poisson case. We propose some total variation (TV) based regularization techniques adapted to the case of Poisson data, which we derive from approximations of logarithmic a-posteriori probabilities. In order to guarantee sharp edges we avoid the smoothing of the total variation and use a dual approach for the numerical solution. We illustrate and test the feasibility of our approaches for data in positron emission tomography, namely reconstructions of cardiac structures with 18F-FDG and H O tracers, respectively.

Original languageEnglish
Title of host publicationComputer Analysis of Images and Patterns - 13th International Conference, CAIP 2009, Proceedings
Number of pages8
Publication statusPublished - 28 Sept 2009
Externally publishedYes
Event13th International Conference on Computer Analysis of Images and Patterns, CAIP 2009 - Munster, Germany
Duration: 2 Sept 20094 Sept 2009
Conference number: 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5702 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th International Conference on Computer Analysis of Images and Patterns, CAIP 2009
Abbreviated titleCAIP 2009


  • Denoising
  • Poisson noise
  • Positron emission tomography
  • Regularization techniques
  • Segmentation
  • Total variation


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