Relationships between the Phase Retrieval Problem and Permutation Invariant Embeddings

06/21/2023

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by   Radu Balan, et al.

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This paper discusses the connection between the phase retrieval problem and permutation invariant embeddings. We show that the real phase retrieval problem for ℝ^d/O(1) is equivalent to Euclidean embeddings of the quotient space ℝ^2× 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.