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

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  • Qi Luo
  • Hongxia Wang

Abstract

Inspired by the implementation of the fractional Fourier transform (FRFT) and its applications in optics, we address the problem of reconstructing a signal from its several FRFT magnitudes (or intensities). The matrix 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 the matrix 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.

Suggested Citation

  • Qi Luo & Hongxia Wang, 2016. "The Matrix Completion Method for Phase Retrieval from Fractional Fourier Transform Magnitudes," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-6, November.
    • Handle: RePEc:hin:jnlmpe:4617327
    DOI: 10.1155/2016/4617327
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