Super-resolution phase retrieval is an inverse problem that appears in diffractive optical imaging (DOI) and consists in estimating a high-resolution image from low-resolution phaseless measurements. DOI has three diffraction zones where the data can be acquired, known as near, middle, and far fields. Recent works have studied super-resolution phase retrieval under a setup that records coded diffraction patterns at the near and far fields. However, the attainable resolution of the image is mainly governed by the sensor characteristics, whose cost increases in proportion to the resolution. Also, these methodologies lack theoretical analysis. Hence, this work derives super-resolution models from low-resolution coded phaseless measurements at any diffraction zone that in contrast to prior contributions, the attainable resolution of the image is determined by the resolution of the coded aperture. For the proposed models, the existence of a unique solution (up to a global unimodular constant) is guaranteed with high probability, which can be increased by designing the coded aperture. Therefore, a strategy that designs the spatial distribution of the coded aperture is developed. Additionally, a super-resolution phase retrieval algorithm that minimizes a smoothed nonconvex least-squares objective function is proposed. The method first approximates the image by a spectral algorithm, which is then refined based upon a sequence of alternate steps. Simulation results show that the proposed algorithm overcomes state-of-the-art methods in reconstructing the high-resolution image. In addition, the reconstruction quality using designed coded apertures is higher than that of the non-designed ensembles.

中文翻译：

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从设计的编码衍射图样中进行超分辨率相位检索。

超分辨率相位检索是一个逆问题，出现在衍射光学成像（DOI）中，主要在于从低分辨率无相位测量中估计高分辨率图像。DOI具有三个可以获取数据的衍射区，称为近场，中场和远场。最近的工作已经研究了在近场和远场记录编码衍射图样的设置下的超分辨率相位检索。然而，图像的可获得分辨率主要由传感器特性决定，其成本与分辨率成比例地增加。而且，这些方法缺乏理论分析。因此，这项工作是通过在任何衍射区域进行低分辨率编码的无相位测量而得出的超分辨率模型，与先前的贡献相反，图像可获得的分辨率取决于编码光圈的分辨率。对于所提出的模型，以高的概率保证了唯一解的存在（高达全局单模常数），可以通过设计编码孔径来增加这种唯一解。因此，开发了一种设计编码孔径的空间分布的策略。此外，提出了一种超分辨率相位检索算法，该算法可最小化平滑的非凸最小二乘目标函数。该方法首先通过光谱算法对图像进行逼近，然后基于一系列可选步骤对其进行精炼。仿真结果表明，该算法克服了现有的高分辨率图像重建方法。此外，