Hengyong Yu and Ge Wang 2009 Phys. Med. Biol. 54 2791 doi:10.1088/0031-9155/54/9/014
Hengyong Yu and Ge Wang
Show affiliationsWhile 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.
Issue 9 (7 May 2009)
Received 7 January 2009, in final form 13 March 2009
Published 15 April 2009
A Corrigendum for this article has been published in 2009 Phys. Med. Biol. 54 4341
Hengyong Yu and Ge Wang 2009 Phys. Med. Biol. 54 2791
Andrea Donini et al JHEP08(2009)041