Journal
INVERSE PROBLEMS
Volume 26, Issue 3, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0266-5611/26/3/035013
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Funding
- NSFC [60325101, 60532080, 60628102, 60872078]
- Key Laboratory of Machine Perception (Ministry of Education) of Peking University
- Microsoft Research of Asia
- NIH/NIBIB [EB002667, EB004287, EB007288]
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Recently, an accurate solution to the interior problem was proposed based on the total variation (TV) minimization, assuming that a region of interest (ROI) is piecewise constant. In this paper, we generalize that assumption to allow a piecewise polynomial ROI, introduce the high-order TV (HOT), and prove that an ROI can be accurately reconstructed from projection data associated with x-rays through the ROI via the HOT minimization if the ROI is piecewise polynomial. Then, we verify our theoretical results in numerical simulation.
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