Signal reconstruction from noisy-phase and -magnitude data

Signal reconstruction based on knowing either the magnitude or the phase of the Fourier transform of the signal is important in numerous applications, and the problem of signal reconstruction from noisy-phase and noisy-magnitude data is addressed. The proposed procedure relates to the deviations of the available magnitude and phase estimates from their exact values in the reconstruction algorithm by use of spectral prototype constraint sets. The properties of these new constraint sets for the magnitude and the phase of the Fourier transform are analyzed, and the corresponding projection operators are constructed. Simulation results indicate improvement of the performance of reconstructions from noisy-phase and -magnitude values based on these sets.