An algorithm for signal reconstruction from bispectrum

The author presents a procedure for reconstructing the impulse response of a minimum- or nonminimum-phase linear time-invariant (LTI) system from its bispectrum. The algorithm is iterative and uses the method of projections onto convex sets (POCS). Prior information such as an energy bound on the impulse response sequence of the LTI system can be incorporated into the algorithm. Corresponding to a given bispectrum and other prior information such as energy, closed and convex sets in an inner product space are constructed. The iterative algorithm consists of successively projecting an initial guess onto these closed and convex sets. Convergence of the algorithm regardless of the initial guess is assured. An algorithm that employs energy information was found to produce better results in simulation that one that ignores energy constraints