Tiny a priori knowledge solves the interior problem in computed tomography
Tiny a priori knowledge solves the interior problem in computed tomography
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DOI：
10.1088/0031-9155/53/9/001
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发表时间：
2008-05-07
影响因子：
3.5
通讯作者：
Defrise, Michel
中科院分区：
文献类型：
--
作者：
Kudo, Hiroyuki;Courdurier, Matias;Defrise, Michel
基于差分反投影（DBP）的概念，（诺奥等人2004年物理医学生物学49 3903，潘等人2005年医学物理32 673，德弗里斯等人2006年逆问题22 1037），本文表明，如果对对象f（x，y）的形式，即f（x，y）在位于感兴趣区域内的小区域上是已知的。此外，我们提出的唯一性结果，以获得更一般的唯一性结果，可以适用于更广泛的一类成像配置。我们还开发了一种重建算法，可以被认为是由Defrise等人（2006年逆问题22 1037）描述的DBP-POCS（投影到凸集）方法的扩展，其中我们不仅将该方法扩展到内部问题，而且还引入了一种新的POCS算法，以减少计算成本。最后，我们提出的实验结果表明，每个获得的唯一性结果对应的反演是稳定的。
Based on the concept of differentiated backprojection (DBP) (Noo et al 2004 Phys. Med. Biol. 49 3903, Pan et al 2005 Med. Phys. 32 673, Defrise et al 2006 Inverse Problems 22 1037), this paper shows that the solution to the interior problem in computed tomography is unique if a tiny a priori knowledge on the object f (x, y) is available in the form that f (x, y) is known on a small region located inside the region of interest. Furthermore, we advance the uniqueness result to obtain more general uniqueness results which can be applied to a wider class of imaging configurations. We also develop a reconstruction algorithm which can be considered an extension of the DBP-POCS (projection onto convex sets) method described by Defrise et al (2006 Inverse Problems 22 1037), where we not only extend this method to the interior problem but also introduce a new POCS algorithm to reduce computational cost. Finally, we present experimental results which show evidence that the inversion corresponding to each obtained uniqueness result is stable.