Feasibility of tomography with unknown view angles
Feasibility of tomography with unknown view angles
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DOI：
10.1109/83.846252
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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，通常假定获得投影的角度是已知的。然而，我们最近已经证明，在相当温和的条件下，这些视角可以从投影本身独特地恢复出来。在这篇文章中，我们讨论了利用投影矩来解决角度恢复问题的这种解的可靠性问题。我们证明了在较温和的条件下，角恢复问题有唯一解，并且对于数据中的扰动是稳定的。此外，当投影被加性高斯噪声破坏时，我们确定了角度估计的方差的Cramer-Rao下界。我们还处理了每个投影偏移某个未知量的情况，这些未知量必须与视角联合估计。受稳定性结果和误差界相对较小的启发，我们构造了一个简单的算法来逼近最大似然估计，并证明了在存在噪声的情况下该问题是可行的。使用这种简单的估计器对各种幻象进行的仿真显示，在中低噪声水平下表现出优异的性能，基本上达到了Cramer-Rao的界限。
In the standard two-dimensional (2-D) parallel beam tomographic formulation, it is generally assumed that the angles at which the projections were acquired are known. We have recently demonstrated, however, that under fairly mild conditions these view angles can be uniquely recovered from the projections themselves. In this paper, we address the question of reliability of such solutions to the angle recovery problem using moments of the projections. We demonstrate that under mild conditions, the angle recovery problem has unique solutions and is stable with respect to perturbations in the data. Furthermore, we determine the Cramer-Rao lower bounds on the variance of the estimates of the angles when the projection are corrupted by additive Gaussian noise. We also treat the case in which each projection is shifted by some unknown amount which must be jointly estimated with the view angles. Motivated by the stability results and relatively small values of the error bounds, we construct a simple algorithm to approximate the ML estimator and demonstrate that the problem can be feasibly solved in the presence of noise. Simulations using this simple estimator on a variety of phantoms show excellent performance at low to moderate noise levels, essentially achieving the Cramer-Rao bounds.