Solving systems of phaseless equations via Kaczmarz methods: A proof of concept study
For researchers in signal processing and imaging, this provides a more efficient iterative method for phase retrieval problems.
The paper extends Kaczmarz methods to solve systems of quadratic equations for phase retrieval, demonstrating computational advantages over state-of-the-art algorithms in both measurement efficiency and computation time.
We study the Kaczmarz methods for solving systems of quadratic equations, i.e., the generalized phase retrieval problem. The methods extend the Kaczmarz methods for solving systems of linear equations by integrating a phase selection heuristic in each iteration and overall have the same per iteration computational complexity. Extensive empirical performance comparisons establish the computational advantages of the Kaczmarz methods over other state-of-the-art phase retrieval algorithms both in terms of the number of measurements needed for successful recovery and in terms of computation time. Preliminary convergence analysis is presented for the randomized Kaczmarz methods.