Relationships between the Phase Retrieval Problem and Permutation Invariant Embeddings

Radu Balan; Efstratios Tsoukanis

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arXiv · 2306.13111

Relationships between the Phase Retrieval Problem and Permutation Invariant Embeddings

Radu Balan·Efstratios Tsoukanis

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Abstract

This paper discusses the connection between the phase retrieval problem and permutation invariant embeddings. We show that the real phase retrieval problem for $\mathbb{R}^d/O(1)$ is equivalent to Euclidean embeddings of the quotient space $\mathbb{R}^{2\times d}/S_2$ performed by the sorting encoder introduced in an earlier work. In addition, this relationship provides us with inversion algorithms of the orbits induced by the group of permutation matrices.

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Radu Balan, Efstratios Tsoukanis. 2023-06-21. Relationships between the Phase Retrieval Problem and Permutation Invariant Embeddings. https://arxiv.org/abs/2306.13111

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