Irregular sampling theory and scattered-center radial Gaussian networks

Several new theorems in network approximation theory indicate that the use of a regular lattice for the centers of a radial basis function expansion may be very conservative in certain situations. The need for a regular grid is relaxed in the present work by using irregular sampling theory to extend the Gaussian network construction procedure. In particular, it is shown that if the chosen sample points correspond to frequencies of complex exponentials which form a frame for a square integrable function defined on a compact neighborhood of the origin K_Δ⊂R^d, the ability of the resulting radial Gaussian network expansion to approximate functions bandlimited to K_Δ can be quantified, and the individual contributions of each network parameter to the approximation identified