Blind identification of two dimensional Volterra models using minimax type of optimization and higher-order cumulants

In this contribution, we further examine our previous studies on the nonlinear texture image modelling based on Volterra series. The observed image, which is assumed to be expressed as an output of a two dimensional Volterra filter driven by a Gaussian input image, is corrupted by an independent Gaussian random noise. Both of the input image and filter parameters are unknown and hence, the problem can be classified as blind system identification. To estimate the unknown parameters, we formulate the equations that relate the parameters of the image model with the cumulant properties of the observed output image. The solution of the formulated equations which are highly nonlinear, is achieved through minimax type of optimization.