Grid filters for local nonlinear image restoration

We describe a new approach to local nonlinear image restoration, based on approximating functions using a regular grid of points in a many-dimensional space. Symmetry reductions and compression of the sparse grid make it feasible to work with eight-dimensional grids as large as 14⁸. Unlike polynomials and neural networks whose filtering complexity per pixel is linear in the number of filter coefficients, grid filters have O(1) complexity per pixel. Grid filters require only a single presentation of the training samples, are numerically stable, leave unusual image features unchanged, and are a superset of order statistic filters. Results are presented for blurring and additive noise