High Order Total Variation Minimization for Interior Tomography.
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 through the HOT minimization if the ROI is piecewise polynomial. Then, we verify our theoretical results in numerical simulation.
Yang
Jiansheng
J
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China.
Yu
Hengyong
H
Jiang
Ming
M
Wang
Ge
G
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