Solving the phase-retrieval problem of a complex signal in the fractional Fourier domain by nonlinear least-squares.

From the viewpoint of unconstrained optimization the phase-retrieval problem of a 1D complex signal in the fractional Fourier domain is formulated as a nonlinear least-squares problem. A definition of the discrete fractional Fourier transform (DFRFT) constructed by a discrete Hermite-Gaussian function is adopted here. The ill-posedness of the problem is stressed, and the Levenberg-Marquardt algorithm of Moré's form is used to solve it.