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Transform-domain Penalized-likelihood Filtering Of Tomographic Data

机译:层析数据的变换域罚似然滤波

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摘要

We present motivation for performing the filtering step of the widely used filtered back-projection algorithm in a non-Radon domain. For square-error optimal penalized-likelihood regularization, filtering in a domain for which the true projection data is sparse in the angle dimension yields coefficients that are more faithful to the ideal filtered data than directly filtering the observed Radon-domain data. In contrast to traditional regularization techniques that filter each projection independently, the proposed filtering technique delivers improved reconstructions by exploiting the correlation of the data in the angle dimension. This enables meaningful reconstructions to be created even from very noisy projection data. In addition, this approach allows for simple penalty matrices to be constructed, enables penalty coefficient to be calculated in a straightforward manner, and results in an easily computed, closed-form solution for the regularizing filters.
机译:我们提出了在非Radon域中执行广泛使用的滤波反投影算法的滤波步骤的动机。对于平方误差最佳罚似然正则化,在角度尺寸上真实投影数据稀疏的域中进行滤波所产生的系数比直接对观测到的Radon域数据进行滤波时更忠实于理想滤波数据。与传统的分别对每个投影进行滤波的正则化技术相比,所提出的滤波技术通过利用角度维度中数据的相关性来提供改进的重构。这样即使从非常嘈杂的投影数据中也可以创建有意义的重建。另外,该方法允许构造简单的罚矩阵,使罚系数能够以直接的方式计算,并且导致用于正则化滤波器的容易计算的闭合形式的解决方案。

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