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.

中文翻译：

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内部断层扫描的高阶总变异最小化

最近，假设感兴趣区域 (ROI) 是分段常数，基于总变差 (TV) 最小化提出了内部问题的准确解决方案。在本文中，我们概括了该假设以允许分段多项式 ROI，引入高阶 TV (HOT)，并证明可以通过 HOT 最小化从与 X 射线相关的投影数据中通过 HOT 最小化来准确地重建 ROI ROI 是分段多项式。然后，我们在数值模拟中验证了我们的理论结果。