Joint image reconstruction and segmentation using the Potts model

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori k...

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Bibliographic Details
Published inInverse problems Vol. 31; no. 2; pp. 25003 - 25031
Main Authors Storath, Martin, Weinmann, Andreas, Frikel, Jürgen, Unser, Michael
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.02.2015
Subjects
Blurred
Image reconstruction
image segmentation
Inverse
photoacoustic tomography
piecewise-constant Mumford-Shah model
Potts model
Radon
Radon transform
Segmentation
Segments
spherical Radon transform
Splitting
Tomography
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Summary:We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from seven angular views only. We illustrate the practical applicability on a real positron emission tomography dataset. As further applications, we consider spherical Radon data as well as blurred data.
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ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/31/2/025003