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. >

[1]  A. Oppenheim,et al.  Signal synthesis and reconstruction from partial Fourier-domain information , 1983 .

[2]  J. Fienup.  Space Object Imaging Through The Turbulent Atmosphere , 1979 .

[3]  Amir Dembo,et al.  Signal synthesis from modified discrete short-time transform , 1988, IEEE Trans. Acoust. Speech Signal Process..

[4]  M. Hayes,et al.  Convergence of iterative nonexpansive signal reconstruction algorithms , 1981 .

[5]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[6]  Jae Lim,et al.  Signal reconstruction from short-time Fourier transform magnitude , 1983 .

[7]  Z. Opial.  Weak convergence of the sequence of successive approximations for nonexpansive mappings , 1967 .

[8]  R. Marks,et al.  Signal synthesis in the presence of an inconsistent set of constraints , 1985 .

[9]  A. Oppenheim,et al.  Signal reconstruction from phase or magnitude , 1980 .

[10]  Jae Lim,et al.  Signal estimation from modified short-time Fourier transform , 1984 .

[11]  D. Youla,et al.  Image Restoration by the Method of Convex Projections: Part 1ߞTheory , 1982, IEEE Transactions on Medical Imaging.

[12]  Ronald E. Crochiere,et al.  A weighted overlap-add method of short-time Fourier analysis/Synthesis , 1980 .

[13]  Jae S. Lim,et al.  Signal reconstruction from Fourier transform sign information , 1985, IEEE Trans. Acoust. Speech Signal Process..

[14]  T. Parks,et al.  Reconstruction of signals from phase: Efficient algorithms, segmentation, and generalizations , 1983 .

[15]  J. Lim,et al.  Effects of additive noise on signal reconstruction from Fourier transform phase , 1983 .

[16]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[17]  Rajendra Kumar,et al.  A fast algorithm for solving a Toeplitz system of equations , 1983, IEEE Trans. Acoust. Speech Signal Process..

[18]  David Malah,et al.  An algebraic approach to discrete short-time Fourier transform analysis and synthesis , 1984, ICASSP.

[19]  D. Youla,et al.  Extensions of a result on the synthesis of signals in the presence of inconsistent constraints , 1986 .

[20]  Bruce R. Musicus,et al.  Iterative algorithms for optimal signal reconstruction and parameter identification given noisy and incomplete data , 1983, ICASSP.

[21]  M. Hayes.  The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform , 1982 .