Relationships between the Phase Retrieval Problem and Permutation Invariant Embeddings

Radu Balan, Efstratios Tsoukanis

Abstract: 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 $\R^{2\times d}/S_2$ 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.

Submission Type: Full Paper