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

• Published in: Kompʹûternaâ optika Vol. 43; no. 6; pp. 1008 - 1020
• Main Authors: Vlasov, V.V., Konovalov, A.B., Kolchugin, S.V.
• Format: Journal Article
• Language: English
• Published: Samara National Research University 01.12.2019
• Subjects: compressed sensing; correlation coefficient; deviation factor; few-view tomography; image reconstruction and segmentation; potts functional; qr-code; shepp-logan phantom; total variation
• ISSN: 0134-2452; 2412-6179; 2412-6179
• DOI: 10.18287/2412-6179-2019-43-6-1008-1020

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.