通过时域额外信号信息强制一维相位检索中的唯一性
Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain
AI总结：
本文研究了一维相位检索中如何通过时域额外信号信息减少歧义并获得唯一解，证明了有限支持信号可被唯一恢复，并通过相位信息获得类似结果。
摘要：
考虑到离散时间相位检索问题从傅里叶强度恢复信号的模糊性，可以提出问题：我们还需要关于未知信号的哪些额外信息才能在大量解集中选择正确解？基于对发生歧义的特征化，我们研究了不同的先验条件，以减少歧义数量甚至获得唯一解。特别地，如果我们能够获取未知信号在时域中的额外幅度信息，我们可以证明几乎所有具有有限支持的信号都能被唯一恢复。此外，我们证明通过利用额外的相位信息也可以获得类似的结果。
英文摘要：
Considering the ambiguousness of the discrete-time phase retrieval problem to recover a signal from its Fourier intensities, one can ask the question: what additional information about the unknown signal do we need to select the correct solution within the large solution set? Based on a characterization of the occurring ambiguities, we investigate different a priori conditions in order to reduce the number of ambiguities or even to receive a unique solution. Particularly, if we have access to additional magnitudes of the unknown signal in the time domain, we can show that almost all signals with finite support can be uniquely recovered. Moreover, we prove that an analogous result can be obtained by exploiting additional phase information.
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。
