Iterative reconstruction of multidimensional signals from nonuniformly spaced samples

A number of different methods for reconstruction of bandlimited 1-D and 2-D signals from nonuniformly spaced samples are compared experimentally. The six 1-D algorithms are solution for Fourier series coefficients, two methods due to Yen, Papoulis´ coordinate transformation, cubic splines, and an iterative method similar to those of Wiley and Gerchberg. Three of the 2-D algorithms are iterative. They differ in the mode of space domain error correction. The fourth 2-D algorithm is the thin-plate splines method. The methods are evaluated on the basis of mean signal-to-error energy ratios calculated over an ensemble consisting of reconstructions of several functions, each sampled with many different random point sets. Sample plots of reconstructions are also included.