Identification of multidimensional and multichannel models using higher order cumulants and bootstrapping techniques in the estimation of higher order cumulants

This thesis deals with the investigation of two topics in signal processing with higher-order statistics. The identification of Moving Average Autoregressive (MA-AR) Multichannel and Multidimensional systems and bootstrapping techniques in the estimation of higher-order cumulants are carried out. A compact Kronecker-product based representation is applied and the definitions of higher-order cumulants and Polyspectra are extended to vector stochastic fields. A new generalized and unified approach to identify the parameters of non-causal and non-Gaussian MA-AR models for multidimensional systems using only output data has been developed. Contrary to autocorrelation based multichannel & multidimensional modeling methods, the MA-AR model in our methods is allowed to be non-minimum phase, asymmetric non-causal and/or non-separable. The problem is transformed to one of estimating the parameters of a pair of MA models. Then, an algorithm for identifying multichannel and multidimensional non-causal as well causal MA models is introduced. The proposed method is applicable to both stochastic and deterministic type problems and can be useful in modeling and restoration of colour images. The bootstrap method has been introduced for the investigation of higher-order cumulant estimates from short data records. The method may be a powerful tool in dealing with the high variance encountered in the estimation of higher-order cumulant. Algorithms for the calculation of the standard deviation and the confidence interval of cumulant estimates have been developed. Based on the algorithms, a method for the estimation of an...