一维相位恢复与额外干涉测量
One-dimensional phase retrieval with additional interference measurements
AI总结：
本文研究了一维相位恢复问题，通过利用额外的干涉测量来实现信号的唯一恢复，解决了传统方法中因相位信息缺失导致的歧义问题。
摘要：
一维相位恢复问题是指从信号的傅里叶强度中恢复复值信号。由于该问题的固有歧义性，确定原始信号在广阔的解集中的挑战性很大，通常需要合适的先验假设或关于未知信号的额外信息。根据应用需求，有时可以访问未知信号与参考信号之间的额外干涉测量。从离散时间设置开始，我们证明每个信号可以从其傅里叶强度和两个额外的干涉测量（未知信号与自身调制信号之间的干涉）中唯一恢复。随后，我们考虑连续时间问题，其中我们获得等效结果。此外，通过使用与未知信号无关的已知或未知参考信号的干涉测量，也可以确保连续时间信号的唯一恢复。
英文摘要：
The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive solution set is challenging and can only be done under suitable a priori assumption or additional information about the unknown signal. Depending on the application, one has sometimes access to further interference measurements between the unknown signal and a reference signal. Beginning with the reconstruction in the discrete-time setting, we show that each signal can be uniquely recovered from its Fourier intensity and two further interference measurements between the unknown signal and a modulation of the signal itself. Afterwards, we consider the continuous-time problem, where we obtain an equivalent result. Moreover, the unique recovery of a continuous-time signal can also be ensured by using interference measurements with a known or an unknown reference which is unrelated to the unknown signal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
