Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is highly ill-posed due to the phase-induced ambiguities and the large number of possible images that can fit to the given measurements. Thus, there's a rich history of enforcing structural priors to improve solutions including sparsity priors and deep-learning-based generative models. However, such priors are often limited in their representational capacity or generalizability to slightly different distributions. Recent advancements in using denoisers as regularizers for non-convex optimization algorithms have shown promising performance and generalization. We present a way of leveraging the prior implicitly learned by a denoiser to solve phase retrieval problems by incorporating it in a classical alternating minimization framework. Compared to performant denoising-based algorithms for phase retrieval, we showcase competitive performance with Fourier measurements on in-distribution images and notable improvement on out-of-distribution images.
翻译:阶段检索是一个非线性反的问题,它需要从它的Fourier级测量中恢复真正的信号。它出现在许多应用中,例如天文成像、X光晶体学、显微镜学等等。由于阶段引起的模糊性以及大量可能适合给定测量的图像,这个问题非常不恰当。因此,在实施结构性前期改进解决方案,包括偏移前程和深学习的基因化模型方面,存在着丰富的历史。然而,这些前期的反映能力或一般性往往局限于略有不同的分布。最近使用Demoiser作为非cavex优化算法的规范工具的进展显示了有希望的性能和一般化。我们展示了一种方法,即利用一个拆调器的隐性知识,通过将它纳入一个传统的交替最小化框架来解决阶段检索问题。相比,我们比较了基于分流法的分阶段检索,我们展示了具有竞争力的性能,在分布图象上进行了四倍的测量,并显著改进了分流图像。