Estimation of linear parametric models of nonGaussian discreterandom fields with application to texture synthesis

A general (possibly asymmetric noncausal and/or nonminimum phase) 2D autoregressive moving average random field model driven by an independent and identically distributed 2D nonGaussian sequence is considered. The model is restricted to be invertible, i.e., system zeros are not allowed to lie on the unit bicircle. Three performance criteria are investigated for parameter estimation of the system parameters given only the output measurements (image pixels). The proposed criteria are functions of the higher order cumulant statistics of an inverse filter output. One of these criteria is novel and the others have been considered in past only for moving average inverses and without any analysis of their consistency. In the paper 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 also analyzed. Experimental results involving synthesized as well as real life textures are presented to illustrate the performance of two of the considered approaches. Experimental results of synthesis of 128x128 textures visually resembling several real life textures in the Brodatz album (and other sources) are presented.