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research article

Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements

Weinmann, Andreas
•
Storath, Martin
2015
Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences

Signals with discontinuities appear in many problems in the applied sciences ranging from mechanics, electrical engineering to biology and medicine. The concrete data acquired are typically discrete, indirect and noisy measurements of some quantities describing the signal under consideration. The task is to restore the signal and, in particular, the discontinuities. In this respect, classical methods perform rather poor, whereas non-convex non-smooth variational methods seem to be the correct choice. Examples are methods based on Mumford-Shah and piecewise constant Mumford-Shah functionals and discretized versions which are known as Blake-Zisserman and Potts functionals. Owing to their non-convexity, minimization of such functionals is challenging. In this paper, we propose a new iterative minimization strategy for Blake-Zisserman as well as Potts functionals and a related jump-sparsity problem dealing with indirect, noisy measurements. We provide a convergence analysis and underpin our findings with numerical experiments.

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Type
research article
DOI
10.1098/rspa.2014.0638
Web of Science ID

WOS:000351236200004

Author(s)
Weinmann, Andreas
Storath, Martin
Date Issued

2015

Publisher

Royal Soc

Published in
Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences
Volume

471

Issue

2176

Article Number

20140638

Subjects

signals with discontinuities

•

piecewise constant signals

•

Potts functionals

•

Blake-Zisserman functionals

•

inverse problems

•

convergence analysis

URL

URL

http://bigwww.epfl.ch/publications/weinmann1501.html
Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LIB  
Available on Infoscience
May 29, 2015
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/114296
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