arXiv Open Access 2023

Finite alphabet phase retrieval

Tamir Bendory Dan Edidin Ivan Gonzalez

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Abstrak

We consider the finite alphabet phase retrieval problem: recovering a signal whose entries lie in a small alphabet of possible values from its Fourier magnitudes. This problem arises in the celebrated technology of X-ray crystallography to determine the atomic structure of biological molecules. Our main result states that for generic values of the alphabet, two signals have the same Fourier magnitudes if and only if several partitions have the same difference sets. Thus, the finite alphabet phase retrieval problem reduces to the combinatorial problem of determining a signal from those difference sets. Notably, this result holds true when one of the letters of the alphabet is zero, namely, for sparse signals with finite alphabet, which is the situation in X-ray crystallography.

Topik & Kata Kunci

cs.IT eess.SP math.AG

Penulis (3)

Tamir Bendory

Dan Edidin

Ivan Gonzalez

Format Sitasi

APA MLA BibTeX

Bendory, T., Edidin, D., Gonzalez, I. (2023). Finite alphabet phase retrieval. https://arxiv.org/abs/2301.10647

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓