Strobl22

Applied Harmonic Analysis and Friends

June 19th - 25th 2022

Strobl, AUSTRIA

"Recovery guarantees for phase retrieval via the randomized Kaczmarz algorithm"

Römer, Patricia

We consider the problem of phase retrieval, i.e., the problem of recovering an object from a system of quadratic equations. As a method for solving such a phase retrieval problem, we investigate a variant of the randomized Kaczmarz algorithm. The main contribution of our work is a recovery guarantee for phase retrieval via the randomized Kaczmarz algorithm from measurements perturbed with additive noise. We consider measurement vectors which are drawn independently and uniformly at random from the unit sphere and suppose that the number of measurements is a sufficiently large multiple of the dimension. We show that, with high probability, the randomized Kaczmarz algorithm achieves convergence up to a neighborhood around the ground-truth solution whose radius depends on the level of the noise.
http://univie.ac.at/projektservice-mathematik/e/talks/Römer_2022-02_Abstract Patricia Römer.pdf

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