Estimation of linear parametric models of non-Gaussian discrete random fields

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Abstract
Finite-dimensional linear parametric models for multidimensional random signals have been found useful in many applications such as image coding, enhancement, restoration, synthesis, classification,a nd spectral estimation. A vast majority of this work is based upon exploitation of only the second-order statistics of the data either explicitly or implicitly. A consequence of this is that either the underlying models should be quarter-plane (or, half plane) causal and minimum phase, or the impulse response of the underlying parametric model must possess certain symmetry (such as 'symmetric noncausality'), in order to achieve parameter identifiability. I consider a general (possibly asymmetric noncausal and/or nonminimum phase) 2D autoregressive moving average random field model driven by an independent and identically distributed 2D non-Gaussian sequence. Several novel performance criteria are proposed and analyzed for parameter estimation of the system parameters given only the output measurements (image pixels). The proposed criteria exploit the higher order cumulant statistics of the data and are sensitive to the magnitude as well as phase of the underlying stochastic image model.

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