1. An overlapping planar approximation method for reducing digital image noise in multi-band digital images comprising the steps of: (a) selecting a target pixel (which is a vector with a number of components equal to the number of bands in the image) from a set of pixels representing an image of interest; (b) selecting a neighborhood of the target pixel; (c) computing a least squares best fit plane of pixel vectors for the selected neighborhood of step b to provide-a goodness of fit (X.sup.2) and an estimated vector value of the target pixel; (d) iterating steps b and c for various types (sizes) and positions of neighborhoods of the target pixel; (e) summing all estimated values of the target pixel with weights based on the goodness of fit (X.sup.2) to provide an output image pixel for the target position; and (f) iterating steps a through e for all pixels from the image of interest, so as to form a set of reduced noise image pixels.