Phase retrieval and system identification in dynamical sampling via Prony’s method

Abstract Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect frame, i.e., sequence of vectors constructed by repeated action operator. The loss phase here turns well-posed into severe ill-posed inverse problem. In existing literature, involved operator usually completely known. this paper, we combine identification system. For instance, if frame based on convolution, then want recover convolution kernel advance. Using Prony’s method, establish several recovery guarantees for and system, whose proofs are constructive yield algebraic methods. required assumptions satisfied almost all signals, operators, vectors. Studying sensitivity procedures, error bounds approximate Prony method complex exponential sums.