相位恢复中先验知识的设计与应用
Designing and using prior knowledge for phase retrieval
摘要：
在这项工作中，我们开发了一种算法，从其傅立叶变换的幅度信号重建的情况下，寻求信号的一些（非零）部分是已知的。虽然我们的方法不假设已知部分包括所寻求的信号的边界，但在显微镜中通常是这种情况：将样本放置在已知掩模内，该掩模可以被认为是包围未知信号的已知光源。因此，在过去，提出了几种算法来解决假设已知边界值的相位恢复问题。与我们的方法不同，这些方法确实依赖于已知部分在边界上的事实。除了重建方法，我们给出了在以前的工作中观察到的现象的解释：重建是快得多时，有更多的能量集中在已知部分。非常令人惊讶的是，这可以解释使用我们以前的结果与近似已知的傅立叶相位的相位恢复。
英文摘要：
In this work we develop an algorithm for signal reconstruction from the magnitude of its Fourier transform in a situation where some (non-zero) parts of the sought signal are known. Although our method does not assume that the known part comprises the boundary of the sought signal, this is often the case in microscopy: a specimen is placed inside a known mask, which can be thought of as a known light source that surrounds the unknown signal. Therefore, in the past, several algorithms were suggested that solve the phase retrieval problem assuming known boundary values. Unlike our method, these methods do rely on the fact that the known part is on the boundary. Besides the reconstruction method we give an explanation of the phenomena observed in previous work: the reconstruction is much faster when there is more energy concentrated in the known part. Quite surprisingly, this can be explained using our previous results on phase retrieval with approximately known Fourier phase.
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