Multiple-filter approach to phase retrieval from modulus data.
A new approach is given for the problem of reconstruction of phase from modulus data. A set of Wiener-filter functions is formed that multiply, in turn, displaced versions of the modulus data (in frequency space) such that the sum is a minimum L(2)-error norm solution for the object. The modulus data are permitted to contain both noise and signal (object) components. The required statistics are power spectra of the signal and noise, and correlations between modulus data at given frequencies and complex object spectral values at adjacent frequencies. In a numerical simulation, a 3 x 3 filter array is used to reconstruct any member of an object class consisting of 16 pictures of space shuttles in various combinations. The 16 pictures are used as a learning set to form the required power spectra and correlations mentioned above. Reconstructions are formed in the presence of data noise, data gaps, and filter-construction noise, in varying amounts. Results are encouraging in that the space shuttle images are always recognizable.
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