BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Joint Reconstruction and Segmentation of Tomographic Data Using the Potts Model

M. Storath

Proceedings of the Third Conference on Applied Inverse Problems (AIP'15), Helsinki, Republic of Finland, May 25-29, 2015, pp. 38.

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 7 angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data.

This is joint work with Andreas Weinmann, Jürgen frikel, and Michael Unser. 

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