Pan X
Department of Radiology, University of Chicago, Illinois 60637, USA.
J Opt Soc Am A Opt Image Sci Vis. 1998 Sep;15(9):2312-26. doi: 10.1364/josaa.15.002312.
In diffraction tomography, the spatial distribution of the scattering object is reconstructed from the measured scattered data. For a scattering object that is illuminated with plane-wave radiation, under the condition of weak scattering one can invoke the Born (or the Rytov) approximation to linearize the equation for the scattered field (or the scattered phase) and derive a relationship between the scattered field (or the scattered phase) and the distribution of the scattering object. Reconstruction methods such as the Fourier domain interpolation methods and the filtered backpropagation method have been developed previously. However, the underlying relationship among and the noise properties of these methods are not evident. We introduce the concepts of ideal and modified sinograms. Analysis of the relationships between, and the noise properties of the two sinograms reveals infinite classes of methods for image reconstruction in diffraction tomography that include the previously proposed methods as special members. The methods in these classes are mathematically identical, but they respond to noise and numerical errors differently.
在衍射层析成像中，散射物体的空间分布是根据测量到的散射数据重建的。对于用平面波辐射照明的散射物体，在弱散射条件下，可以采用玻恩（或里托夫）近似来线性化散射场（或散射相位）的方程，并推导散射场（或散射相位）与散射物体分布之间的关系。诸如傅里叶域插值方法和滤波反传播方法等重建方法此前已得到发展。然而，这些方法之间的潜在关系以及噪声特性并不明显。我们引入了理想和修正正弦图的概念。对这两种正弦图之间的关系及其噪声特性的分析揭示了衍射层析成像中无限类别的图像重建方法，其中包括先前提出的方法作为特殊成员。这些类别中的方法在数学上是相同的，但它们对噪声和数值误差的响应不同。
