Bispectral reconstruction of signals in noise: amplitude reconstruction issues

When we have observations of a discrete deterministic signal (physical object) in colored Gaussian noise, it is possible to obtain asymptotically unbiased estimates of the bispectrum of the signal only at frequency pairs (al, w2) which do not satisfy any of the following: wI = 0, w 2 = 0, and o1 + w2 = 0. Several approaches reported in the literature that deal with magnitude reconstruction from bispectra use bispectrum samples that lie on one of these three straight lines, thus using samples which are biased due to noise. We propose two approaches that rectify this situation. The paper also discusses some of the tradeoffs involved in using bispectrum based reconstruction approaches vis-&vis other techniques. Applications to several types of problems are discussed.