Partial differential equations and finite-difference methods in image processing,part 1: Image representation

Stochastic representation of discrete images by partial differential equation operators is considered. It is shown that these representations can fit random images, with nonseparable, isotropic covariance functions, better than other common covariance models. Application of these models in image restoration, data compression, edge detection, image synthesis, etc., is possible.Different representations based on classification of partial differential equations are considered. Examples on different images show the advantages of using these representations. The previously introduced notion of fast Karhunen-Loeve transform is extended to images with nonseparable or nearly isotropic covariance functions, or both.