Joint Image Reconstruction and Segmentation Using the Potts Model

Abstract

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.

References in corpus (7)

• Natural Scales in Geographical Patterns
• Consistencies and rates of convergence of jump-penalized least squares estimators
• Jump-sparse and sparse recovery using Potts functionals
• A constrained, total-variation minimization algorithm for low-intensity X-ray CT
• Universal inversion formulas for recovering a function from spherical means
• Sparse Stochastic Processes and Discretization of Linear Inverse Problems
• Reconstruction Formulas for Photoacoustic Sectional Imaging

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