Journal
INVERSE PROBLEMS
Volume 35, Issue 5, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-6420/ab0b77
Keywords
image reconstruction; image segmentation; Bregman iteration; non-convex optimisation; magnetic resonance imaging; total variation; iterative regularisation
Categories
Funding
- Cambridge Cancer Centre
- Leverhulme Trust
- EPSRC [EP/M00483X/1, EP/N014588/1]
- Cantab Capital Institute for the Mathematics of Information
- CHiPS (Horizon 2020 RISE project grant)
- NoMADS (Horizon 2020 RISE project grant)
- Alan Turing Institute
- EPSRC [EP/J009539/1, EP/M00483X/1, EP/N014588/1] Funding Source: UKRI
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All imaging modalities such as computed tomography, emission tomography and magnetic resonance imaging 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. Recently, the idea of tackling both problems jointly has been proposed. 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.
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