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On the randomized Kaczmarz algorithm for phase retrieval.
In: (55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021, 31 October - 3 November 2021, Virtual, Pacific Grov). 2022. 847-851 (Conference Record - Asilomar Conference on Signals, Systems and Computers ; 2021-October)
We investigate a variant of the randomized Kaczmarz algorithm as a method for solving the phase retrieval problem. The main contribution of this paper is a recovery guarantee for phase retrieval from measurements perturbed with additive noise via the randomized Kaczmarz algorithm. We consider the scenario that the measurement vectors are drawn independently and uniformly at random from the unit sphere and that the number of measurements is a sufficiently large multiple of the dimension. We show that, with high probability, the randomized Kaczmarz algorithm converges to a neighborhood around the ground-truth solution whose radius depends on the noise level.
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Publication type
Article: Conference contribution
Keywords
Additive Noise ; Kaczmarz Algorithm ; Phase Retrieval
ISSN (print) / ISBN
1058-6393
Conference Title
55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021
Conference Date
31 October - 3 November 2021
Conference Location
Virtual, Pacific Grov
Quellenangaben
Volume: 2021-October,
Pages: 847-851
Non-patent literature
Publications
Institute(s)
Institute of Biological and Medical Imaging (IBMI)
Grants
Helmholtz Association