基于自相关的去卷积图像恢复
Deconvolved Image Restoration from Autocorrelations
摘要：
从自相关中恢复信号，或者等效地，恢复与给定傅立叶模数相关联的相位，是成像中广泛存在的问题。这个问题已经解决了一些实验情况下，从光学显微镜自适应天文学，利用基于约束条件和先验信息的假设恢复对象。以类似的方式，去卷积是成像中的另一个常见问题，特别是在光学界，允许模糊图像的高分辨率重建。在这里，我们解决的混合问题，执行自相关反演，而在同一时间，去卷积其当前的估计。为此，我们提出了一个I-发散优化，驱动我们的形式主义成为一个广泛使用的迭代方案，灵感来自基于贝叶斯的方法。我们展示了从模糊自相关中恢复信号的方法，进一步分析了模糊物体和带限傅立叶测量的情况。
英文摘要：
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.
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