Presence of Cepstral Peak in Random Reflected Ultrasound Signals

A peak in the power cepstrum, or the squared magnitude of the Fourier transform of the data log-power spectrum, is commonly observed when processing reflections from plate-like structures, such as membranes. In this case, the cepstral peak at the smallest nonzero time lag, or quefrency, value can be used to determine the thickness of the plate. For reflections from a medium composed of randomly distributed scatterers, such as liver tissue, a cepstral peak is also commonly observed, but cannot be so intuitively explained as in the deterministic case above. In this paper, it is demonstrated that the presence of a cepstral peak depends on the form of the probability density function (pdf) of the separation between reflectors. In the case where the pdf is uniform from 0 to S_M, the cepstral peak is found to occur at the quefrency corresponding to S_M. For simple unimodal pdfs, a cepstral peak will occur at the location of the maximum probability. These observations are shown analytically and verified through simulations. The diagnostic value of these results lies in the interpretation of the relation of the cepstral peak location to the spacing of the scattering elements in the tissue.