Experimental results on reconstruction of complex multidimensional signals from Fourier transform magnitude
Summary form only given. Reconstruction of multidimensional signals from Fourier transform magnitude (FTM) is viewed as a special case of the reconstruction of a complex signal from the FTM and space domain phase, with the phase being equal to zero or pi . Specifically, pixels above the threshold used for one bit quantization can be thought of as having zero phase, and the ones below it can be considered to have pi phase. In a similar fashion, the problem of reconstruction of real images from FTM can be considered to be a special case of the reconstruction of complex signals from the FTM and space domain phase, with the phase being equal to zero. The author's experimental results indicate that the former reconstruction problem with binary phase is considerably more robust than the latter one with zero phase. Thus, an interesting question to examine would be whether reconstruction of a complex signal from FTM and space-domain phase becomes better conditioned as the space domain phase becomes more randomized. The author's preliminary experiments show that reconstruction from FTM and space domain random phase with uniform probability distribution function results in excellent reconstruction quality, and that the relative importance of FTM information with respect to Fourier transform phase information increases as the randomness of the phase of the complex multidimensional signal in space domain increases.<<ETX>>