Deterministic estimation of the bispectrum and its application to image restoration

While the bispectrum has desirable properties in itself and therefore has a lot of potential to be applied to image restoration, few real-world application results have appeared in the literature. The major problem with this is the difficulty in realizing the expectation operator, due to the lack of realizations. In this paper, the true bispectrum is defined as the expectation of the sample bispectrum, which is the Fourier representation of the triple correlation given one realization. The characteristics of sample bispectrum are analyzed and a way to obtain an estimate of the true bispectrum without stochastic expectation, using the generalized theory of weighted regularization is shown.