Fast algorithms for phase and magnitude reconstruction from bispectra

Abstract

Techniques are developed for signal reconstruction from samples of the bispectrum of a 1-D or 2-D signal. The phase and magnitude of the Fourier transform of a signal as well as those of the bispectrum are expanded into a series using a set of appropriate basis functions. Reconstruction is achieved by equating coefficients of like terms of these two expansions. The algorithms derive their speed by using a restricted portion of the bispectrum space and by being based on the use of the fast Fourier transform. In addition to detailed theoretical derivations, results of computer simulation are provided.