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Phys Med Biol. 2009 May 7;54(9):2791-805. doi: 10.1088/0031-9155/54/9/014. Epub 2009 Apr 15.

Compressed sensing based interior tomography.

Author information

  • 1Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Science, Virginia Tech, Blacksburg, VA 24061, USA. hengyong-yu@ieee.org

Erratum in

  • Phys Med Biol. 2009 Jul 7;54(13):4341.

Abstract

While conventional wisdom is that the interior problem does not have a unique solution, by analytic continuation we recently showed that the interior problem can be uniquely and stably solved if we have a known sub-region inside a region of interest (ROI). However, such a known sub-region is not always readily available, and it is even impossible to find in some cases. Based on compressed sensing theory, here we prove that if an object under reconstruction is essentially piecewise constant, a local ROI can be exactly and stably reconstructed via the total variation minimization. Because many objects in computed tomography (CT) applications can be approximately modeled as piecewise constant, our approach is practically useful and suggests a new research direction for interior tomography. To illustrate the merits of our finding, we develop an iterative interior reconstruction algorithm that minimizes the total variation of a reconstructed image and evaluate the performance in numerical simulation.

PMID:
19369711
[PubMed - indexed for MEDLINE]
PMCID:
PMC2863332
Free PMC Article

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