The Matrix Completion Method for Phase Retrieval from Fractional Fourier Transform Magnitudes

摘要

Inspired by the implementation of the fractional Fourier transform(FRFT) and its applications in optics, we address the problem of reconstructing a signal fromits several FRFT magnitudes (or intensities). Thematrix completion method is adopted here. Through numerical tests, the matrix completion method is proven effective in both noisy and noise-free situations. We also compare our method with the Gerchberg-Saxton (GS) algorithm based on FRFT. Numerical tests show that thematrix completion method gains a certain advantage in recovering uniqueness and convergence over the GS algorithm in the noise-free case. Furthermore, in terms of noisy signals, the matrix completion method performs robustly and adding more measurements can generally increase accuracy of recovered signals.