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The stability of generalized phase retrieval problem over compact groups
The generalized phase retrieval problem over compact groups aims to recover a set of matrices, representing an unknown signal, from their associated Gram matrices, leveraging prior structural knowledge about the signal.
The generalized phase retrieval problem over compact groups
In this broader context, the missing phases in Fourier space are replaced by missing unitary or orthogonal matrices arising from the action of a compact group on a finite-dimensional vector space.
The beltway problem over orthogonal groups
The classical beltway problem entails recovering a set of points from their unordered pairwise distances on the circle.
Phase retrieval with semi-algebraic and ReLU neural network priors
In this paper, we study the phase retrieval problem under the prior that the signal lies in a semi-algebraic set.
Algebraic theory of phase retrieval
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
