Phase retrieval with outliers based on smoothing function

Abstract

This paper studies the problem of recovery signal from the given quadratic measurements that are corrupted by outliers, which is called phase retrieval. We propose a phase retrieval algorithm based on median Smooth Amplitude Flow (median-SAF), which adopts the median orthogonality-promoting initialization method to generate a reasonable initial estimate, and then iteratively update using the median smooth amplitude flow to ensure convergence to the global optimal solution. In the iterative step, we use the amplitude loss function to reduce the number of measurements and introduce the sample median in gradient descent to handle the outliers. Simulation experiments show that the presented algorithm can recover the signal with outliers while the original Smooth Amplitude Flow algorithm cannot do, and compared with other median-based algorithms, the required number of measurements of our algorithm can be fewer and convergence speed is faster.