一位相位恢复：更多的样本意味着更少的复杂性？
One-Bit Phase Retrieval: More Samples Means Less Complexity?
摘要：
相位恢复的经典问题在光学、成像和信号处理等领域有着广泛的应用。在本文中，我们考虑相位恢复问题，在一位设置，信号采样使用一位模数转换器（ADC）。在信号处理系统中部署1位ADC的一个显著优势是，与高分辨率ADC相比，其采样速率更高。这导致在短时间内在ADC输出端收集大量1位样本。我们证明，这种优势支付非凡的红利，当涉及到凸相位检索配方，即经常遇到的矩阵半定约束以及秩约束（这是计算禁止执行），成为多余的相位检索在面对不断增长的样本量。几个数值结果来说明所提出的方法的有效性。
英文摘要：
The classical problem of phase retrieval has found a wide array of applications in optics, imaging and signal processing. In this paper, we consider the phase retrieval problem in a one-bit setting, where the signals are sampled using one-bit analog-to-digital converters (ADCs). A significant advantage of deploying one-bit ADCs in signal processing systems is their superior sampling rates as compared to their high-resolution counterparts. This leads to an enormous amount of one-bit samples gathered at the output of the ADC in a short period of time. We demonstrate that this advantage pays extraordinary dividends when it comes to convex phase retrieval formulations, namely that the often encountered matrix semi-definiteness constraints as well as rank constraints (that are computationally prohibitive to enforce), become redundant for phase retrieval in the face of a growing sample size. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.
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