Nonstationary composite modeling of images

Images are modeled as second-order nonstationary random fields, using a composite model that consists of a space-varying mean value function and a zero-mean nonstationary random field. The first component represents the underlying structure of an image, whereas the residual component provides the image´s fine information. The authors develop space-varying estimators for the mean value and the variance functions and obtain conditions for such estimators to be statistically unbiased and consistent. The residual image component is modeled as an autoregressive system with space-varying coefficients. Identification of these coefficients is accomplished using a complete set of orthonormal basis functions to represent them. An efficient recursive procedure is proposed to solve the normal equations resulting from the minimum-mean square identification. Applications for the proposed modeling procedure can be found in the restoration and coding of images. Examples illustrating some aspects of the procedure and its application to image restoration are given