The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-147

“Modeling and Parameter Estimation of Multidimensional Non-Gaussian Processes Using Cumulants”

by A. Swami, G.B. Giannakis and J.M. Mendel

August 1989

Extending the notion of second-order correlations, we define the cumulants of stationary non-Gaussian random fields, and demonstrate their potential for modeling and reconstruction of multidimensional signals and systems. Cumulants and their Fourier transforms called polyspectra preserve complete amplitude and phase information of a multidimensional linear process, even when it is corrupted by additive colored Gaussian noise of unknown co-variance function. Relying on this property, phase reconstruction algorithms are developed using polyspectra, which can be computed via a 2-D FFT-based algorithm. Additionally, consistent ARMA parameter estimators are derived for identification of linear space-invariant multidimensional models which are driven by unobservable, i.i.d., non-Gaussian random fields. Contrary to autocorrelation based multidimensional modeling approaches, when cumulants are employed, the ARMA model is allowed to be non-minimum phase, asymmetric non-causal or non-separable.

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