论文标题
自相关的反相关图像恢复
Deconvolved Image Restoration from Autocorrelations
论文作者
论文摘要
从自动相关中恢复信号，或等效地检索与给定傅立叶模量链接的相位是成像中的广泛问题。从光学显微镜到适应性天文学，使用基于约束的假设以及有关恢复对象的先验信息，在许多实验情况下都解决了此问题。以类似的方式，反卷积是成像中的另一个常见问题，尤其是在光学群落中，允许高分辨率重建模糊的图像。在这里，我们解决了执行自动相关反演的混合问题，同时否定了当前的估计。为此，我们提出了一种I-Divergence优化，将我们的形式主义推向了一种受贝叶斯方法的启发，将我们的形式主义推向了广泛使用的迭代方案。我们证明了从模糊的自动相关性中恢复信号的方法，进一步分析了对象模糊的情况和带限的傅立叶测量结果。
Recovering a signal from auto-correlations or, equivalently, retrieving the phase linked to a given Fourier modulus, is a wide-spread problem in imaging. This problem has been tackled in a number of experimental situations, from optical microscopy to adaptive astronomy, making use of assumptions based on constraints and prior information about the recovered object. In a similar fashion, deconvolution is another common problem in imaging, in particular within the optical community, allowing high-resolution reconstruction of blurred images. Here we address the mixed problem of performing the auto-correlation inversion while, at the same time, deconvolving its current estimation. To this end, we propose an I-divergence optimization, driving our formalism into a widely used iterative scheme, inspired by Bayesian-based approaches. We demonstrate the method recovering the signal from blurred auto-correlations, further analysing the cases of blurred objects and band-limited Fourier measurements.
