Uniqueness of tomography with unknown view angles
Uniqueness of tomography with unknown view angles
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DOI：
10.1109/83.846251
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发表时间：
2000-06-01
影响因子：
10.6
通讯作者：
Bresler, Y
中科院分区：
文献类型：
--
作者：
Basu, S;Bresler, Y
在标准的二维(2-D)平行波束层析成像公式中，假设获得投影的角度是已知的。然而，在某些情况下，这些角度只能大致知道(例如在移动患者的磁共振成像(MRI)的情况下)，或者完全未知。后者发生在基于电子显微镜的病毒颗粒成像中的三维(3D)版本中，我们解决了在二维平行束情况下直接从投影数据本身确定视角的问题，我们证明了在一些相当温和的条件下，视角是由投影数据唯一确定的。基于Radon变换的Helgasson-Ludwig一致性条件，我们给出了这些Vies角唯一恢复的条件。我们还表明，当投影平移一定的随机量时，必须与视角联合估计，平移和视角的唯一恢复是可能的。
In the standard two-dimensional (2-D) parallel beam tomographic formulation, it is assumed that the angles at which the projections were acquired are known. In certain situations, however, these angles are known only approximately (as in the case of magnetic resonance imaging (MRI) of a moving patient), or are completely unknown. The latter occurs in a three-dimensional (3-D) version of the problem in the electron microscopy-based imaging of viral particles, We address the problem of determining the view angles directly from the projection data itself in the 2-D parallel beam case, We prove the surprising result that under some Fairly mild conditions, the view angles are uniquely determined by the projection data. We present conditions for the unique recovery of these vies angles based on the Helgasson-Ludwig consistency conditions for the Radon transform. We also show that when the projections are shifted by some random amount which must be jointly estimated with the view angles, unique recovery of both the shifts and view angles is possible.