This research is concerned with development, analysis and evaluation of algorithms for signal/image processing in addition to, or in lieu of, the usual second order statistics. Both time series (only system output is observed) and system identification (both input and output are observed) formulations are being considered; and both one-dimensional and multidimensional signals and systems are being investigated. Whereas the second order statistics of signals are a function of only the underlying system transfer function magnitude, higher order Statistics (HOS) of the data carry useful information about the phase characteristics of the underlying signal/system which is crucial in deconvolution problems such as those arising in digital communication channel equalization, seismic wavelet processing, and image restoration, analysis and synthesis. Time domain as well as frequency domain methods using higher order cumulant functions and higher order cumulant spectra (or higher order integrated cumulant spectra), respectively, are being pursued. Among the applications being investigated are: (i) image texture synthesis and classification, (ii) differential time-delay and doppler estimation in unknown spatially correlated Gaussian noise, (iii) blind deconvolution with unknown, possibly nonminimum phase, channels including image restoration, and (iv) system identification with noise inputs.
