Iterative projection approach for phase retrieval of semi-sparse wave field

In the paper, we consider the problem of two-dimensional (2D) phase retrieval, which recovers a 2D complex-valued wave field from magnitudes of both wave field and its Fourier transform. Due to the absence of the phase measurements, prior information on wave field is needed in order to recover phase, which is feasible when the phases of the wave field are sparse. In this paper, we improve the phase retrieval accuracy by incorporating phase sparse constraint of wave field. As a sequel to previous iterative projection approaches, iterative projection approaches with phase sparse constraint are realized based on ‘soft thresholding’. It has superior performances in terms of convergence, residual error, noise stability, and suitability in large-scale phase retrieval problems. Numerical experiments illustrate that the proposed approach outperforms existing iterative projection approaches.

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