SIAM Journal on Imaging Sciences, Volume 14, Issue 2, Page 620-644, January 2021.
In coherent diffraction imaging (CDI) experiments, the intensity of the scattered wave impinging on an object is measured on an array of detectors. These measurements can be interpreted as samples of the square of the modulus of the Fourier transform of the unknown scattering density. A beamstop obstructs the forward scattered wave and, hence, the modulus Fourier data from a neighborhood of $k=0$ cannot be measured. In this note, we describe a linear method for recovering this unmeasured modulus Fourier data from the measured values and an estimate of the support of the image's autocorrelation function without consideration of phase retrieval. We analyze the effects of noise, and the conditioning of this problem, which grows exponentially with the modulus of the maximum spatial frequency not measured.

中文翻译：

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在相干衍射成像中恢复丢失的数据

SIAM影像科学杂志，第14卷，第2期，第620-644页，2021年1月。
在相干衍射成像（CDI）实验中，撞击在物体上的散射波强度是在探测器阵列上测量的。这些测量结果可以解释为未知散射密度的傅立叶变换模量平方的样本。光束阻止器阻挡了前向散射波，因此无法测量来自$ k = 0 $附近的模量傅立叶数据。在本说明中，我们描述了一种线性方法，可从测量值中恢复此未测量的模量傅立叶数据，以及不考虑相位检索的情况下对图像自相关函数支持的估计。我们分析了噪声的影响以及该问题的条件，该问题随着未测量的最大空间频率的模数呈指数增长。