Deconvolution based criteria for parameter estimation of multidimensional non-Gaussian signal models using noisy data

A general (possibly asymmetric noncausal and/or nonminimum phase) two-dimensional autoregressive moving average random field model driven by an independent and identically distributed (i.i.d.) two-dimensional non-Gaussian sequence is considered. A novel class of performance criteria is investigated for parameter estimation of the system parameters given only the noisy output measurements (image pixels). The proposed criteria are functions of the higher-order cumulant statistics of an inverse filter output. Strong consistency of the proposed methods under the assumption that the system order is known is proved. The convergence of the proposed parameter estimators under overparametrization is analyzed