Phase estimation using the bispectrum and its application to image restoration

We propose algorithms for estimating the phase of a deterministic signal using its bispectrum. The bispectrum of a signal is the (discrete) Fourier transform of its triple correlation. While second-order statistics (e.g., correlation function, power spectrum, etc.) do not provide any information about the phase of the signal, third-order statistics (e.g., triple correlation, bispectrum, etc.) allow the recovery of the phase of the signal. We show that the applicability of two commonly used algorithms for phase characteristics. We propose algorithms for estimating the phase of arbitrary signals such as images, by taking into account the ambiguity due to the use of the principal value of the phase component. The resulting estimated phase is incorporated into a restoration filter. Image lines and images are used in our experiments to test the effectiveness of the proposed algorithms.