Joint Image Reconstruction and Segmentation Using the Potts Model

TL;DR

This paper introduces an efficient algorithm for joint image reconstruction and segmentation using the Potts model, capable of handling limited data and avoiding artifacts, demonstrated on Radon and PET data.

Contribution

It presents a novel splitting algorithm for the non-convex Potts problem that does not require prior knowledge of segments or gray levels.

Findings

Successfully reconstructs Shepp-Logan phantom from 7 views

Effective on real PET data and spherical Radon data

Avoids geometric staircasing artifacts

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.