Enhancing joint reconstruction and segmentation with non-convex Bregman iteration

TL;DR

This paper introduces a unified variational framework combining image reconstruction and segmentation, utilizing non-convex Bregman iteration to enhance both processes in medical imaging modalities.

Contribution

It proposes a novel non-convex Bregman iteration method that jointly optimizes reconstruction and segmentation, with a proven convergence scheme, improving over traditional sequential methods.

Findings

Enhanced reconstruction quality on synthetic and real data.

Improved segmentation accuracy compared to classical methods.

Convergence guarantees for the proposed alternating minimisation scheme.

Abstract

All imaging modalities such as computed tomography (CT), emission tomography and magnetic resonance imaging (MRI) require a reconstruction approach to produce an image. A common image processing task for applications that utilise those modalities is image segmentation, typically performed posterior to the reconstruction. We explore a new approach that combines reconstruction and segmentation in a unified framework. We derive a variational model that consists of a total variation regularised reconstruction from undersampled measurements and a Chan-Vese based segmentation. We extend the variational regularisation scheme to a Bregman iteration framework to improve the reconstruction and therefore the segmentation. We develop a novel alternating minimisation scheme that solves the non-convex optimisation problem with provable convergence guarantees. Our results for synthetic and real data show that both reconstruction and segmentation are improved compared to the classical sequential approach.