Automated smoothing of image and other regularly spaced data

This paper is primarily motivated by the problem of automatically removing unwanted noise from high-dimensional remote sensing imagery. The initial step involves the transformation of the data to a space of intrinsically lower dimensionality and the smoothing of images in the new space. Different images require different amounts of smoothing. The signal (assumed to be mostly smooth with relatively few discontinuities) is estimated from the data using the method of generalized cross-validation. It is shown how the generalized cross-validated thin-plate smoothing spline with observations on a regular grid (in d-dimensions) is easily approximated and computed in the Fourier domain. Space domain approximations are also investigated. The technique is applied to some remote sensing data