ONE-DIMENSIONAL TOMOGRAPHY - A COMPARISON OF ABEL, ONION-PEELING, AND FILTERED BACKPROJECTION METHODS
ONE-DIMENSIONAL TOMOGRAPHY - A COMPARISON OF ABEL, ONION-PEELING, AND FILTERED BACKPROJECTION METHODS
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DOI：
10.1364/ao.31.001146
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发表时间：
1992-03-10
期刊：
影响因子：
1.9
通讯作者：
DASCH, CJ
中科院分区：
文献类型：
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作者：
DASCH, CJ
结果表明，在不假设目标被反卷积的情况下，Abel反演、洋葱剥离和滤波后的反投影方法可以相互比较。如果投影数据是在等间距的径向位置上取的，则反卷积场由投影的加权和除以数据间距给出。权重因子与数据间距无关。所有这些方法都非常相似，并且具有阿贝尔行为：径向位置的场主要由径向位置周围几个投影的加权差决定。洋葱剥皮和使用两点插值的阿贝尔反演是相似的。当Shepp-Logan滤波后的反投影方法降维到一维时，它本质上与使用三点插值的Abel反演相同。加权因子直接决定了相对噪声性能：三点Abel反演效果最好，而洋葱剥皮效果最差，噪声约为前者的两倍。基于易于计算，鲁棒性和噪声，三点Abel反演是推荐的。
It is shown that the Abel inversion, onion-peeling, and filtered backprojection methods can be intercompared without assumptions about the object being deconvolved. If the projection data are taken at equally spaced radial positions, the deconvolved field is given by weighted sums of the projections divided by the data spacing. The weighting factors are independent of the data spacing. All the methods are remarkably similar and have Abelian behavior: the field at a radial location is primarily determined by the weighted differences of a few projections around the radial position. Onion-peeling and an Abel inversion using two-point interpolation are similar. When the Shepp-Logan filtered backprojection method is reduced to one dimension, it is essentially identical to an Abel inversion using three-point interpolation. The weighting factors directly determine the relative noise performance: the three-point Abel inversion is the best, while onion peeling is the worst with approximately twice the noise. Based on ease of calculation, robustness, and noise, the three-point Abel inversion is recommended.