Enhancing joint reconstruction and segmentation with non-convex Bregman iteration

Veronica Corona, Martin Benning, Matthias J. Ehrhardt, Lynn F. Gladden, Richard Mair, Andi Reci, Andrew J. Sederman, Stefanie Reichelt, Carola-Bibiane Schoenlieb

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Abstract

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.

Original languageEnglish
Article number055001
Number of pages34
JournalInverse Problems
Volume35
Issue number5
Early online date26 Apr 2019
DOIs
Publication statusPublished - 26 Apr 2019

Keywords

  • Bregman iteration
  • image reconstruction
  • image segmentation
  • iterative regularisation
  • magnetic resonance imaging
  • non-convex optimisation
  • total variation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

Cite this

Corona, V., Benning, M., Ehrhardt, M. J., Gladden, L. F., Mair, R., Reci, A., ... Schoenlieb, C-B. (2019). Enhancing joint reconstruction and segmentation with non-convex Bregman iteration. Inverse Problems, 35(5), [055001]. https://doi.org/10.1088/1361-6420/ab0b77

Enhancing joint reconstruction and segmentation with non-convex Bregman iteration. / Corona, Veronica; Benning, Martin; Ehrhardt, Matthias J.; Gladden, Lynn F.; Mair, Richard; Reci, Andi; Sederman, Andrew J.; Reichelt, Stefanie; Schoenlieb, Carola-Bibiane.

In: Inverse Problems, Vol. 35, No. 5, 055001, 26.04.2019.

Research output: Contribution to journalArticle

Corona, V, Benning, M, Ehrhardt, MJ, Gladden, LF, Mair, R, Reci, A, Sederman, AJ, Reichelt, S & Schoenlieb, C-B 2019, 'Enhancing joint reconstruction and segmentation with non-convex Bregman iteration', Inverse Problems, vol. 35, no. 5, 055001. https://doi.org/10.1088/1361-6420/ab0b77
Corona, Veronica ; Benning, Martin ; Ehrhardt, Matthias J. ; Gladden, Lynn F. ; Mair, Richard ; Reci, Andi ; Sederman, Andrew J. ; Reichelt, Stefanie ; Schoenlieb, Carola-Bibiane. / Enhancing joint reconstruction and segmentation with non-convex Bregman iteration. In: Inverse Problems. 2019 ; Vol. 35, No. 5.
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