Signal reconstruction from noisy partial information of its transform

The usual assumption that the available partial information is noiseless is replaced by a more realistic statistical model which compensates for the presence of noise. The signal reconstruction is thus viewed as a parameter estimation problem, for which the EM iterative algorithm of A.P. Dempster, N.M. Laird, and D.B. Rubin (J. Roy. Stat. Soc., B, vol.39, p.1-37, 1977) is especially suitable. The posterior probability of the signal increases from iteration to iteration, till the signal converges to a stationary point of the posterior distribution. Each iteration involves one transformation followed by an inverse transformation (usually discrete Fourier transformation (DFT) and inverse DFT). Algorithms for reconstruction of both one- and two-dimensional signals from their spectral magnitude, spectral phase, or modified short time Fourier transform are typical examples of the proposed scheme