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Joint image reconstruction and segmentation: Comparison of two algorithms for few-view tomography

V.V. Vlasov1, A.B. Konovalov1, S.V. Kolchugin1

1 Russian Federal Nuclear Center – Zababakhin Institute of Applied Physics,
Chelyabinsk Region, Snezhinsk, 456770, Russia, 13 Vasiliev Str.

 PDF, 1100 kB

DOI: 10.18287/2412-6179-2019-43-6-1008-1020

Pages: 1008-1020.

Full text of article: Russian language.

Abstract:
Two algorithms of few-view tomography are compared, specifically, the iterative Potts minimization algorithm (IPMA) and the algebraic reconstruction technique with TV-regularization and adaptive segmentation (ART-TVS). Both aim to reconstruct piecewise-constant structures, use the compressed sensing theory, and combine image reconstruction and segmentation procedures. Using a numerical experiment, it is shown that either algorithm can exactly reconstruct the Shepp-Logan phantom from as small as 7 views with noise characteristic of the medical applications of X-ray tomography. However, if an object has a complicated high-frequency structure (QR-code), the minimal number of views required for its exact reconstruction increases to 17–21 for ART-TVS and to 32–34 for IPMA. The ART-TVS algorithm developed by the authors is shown to outperform IPMA in reconstruction accuracy and speed and in resistance to abnormally high noise as well. ART-TVS holds good potential for further improvement.

Keywords:
few-view tomography, image reconstruction and segmentation, compressed sensing, Potts functional, total variation, Shepp-Logan phantom, QR-code, correlation coefficient, deviation factor.

Citation:
Vlasov VV, Konovalov AB, Kolchugin SV. Joint image reconstruction and segmentation: Comparison of two algorithms for few-view tomography. Computer Optics 2019; 43(6): 1008-1020. DOI: 10.18287/2412-6179-2019-43-6-1008-1020.

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