A Semicausal Model for Recursive Filtering of Two-Dimensional Images

A two-dimensional discrete stochastic model for representing images is developed. This representation has lower mean square error, compared to a standard autoregressive Markov representation. Application of the model to linear filtering of images degraded by white noise leads to scalar recursive filtering equations requiring only 0(N
²
log
2
N) computations for N x N images. The filter algorithm is a hybrid algorithm where the image is transformed along one dimension and spatially filtered, recursively, in the other. Examples on a 255 X 255 image are given.