A CLASS OF EIGENVALUE PROBLEMS IN INTERPOLATION , EXTRAPOLATION , AND SAMPLINGPaulo

The reconstruction of signals or images from incomplete or noisy data is a recurring problem in signal theory, with important practical applications. The band-limited interpolation and extrapola-tion problems, in which the signals or images are assumed to be band-limited, are among the most often studied reconstruction problems. We discuss certain aspects of these problems, concentrating on the stability of the reconstructions as a function of the sampling set. To do this, the reconstruction problems are formulated in a way which easily leads to several iterative and non-iterative algorithms, which seem to have a number of advantages over some previously known methods. The spectrum of the reconstruction operators is studied, yielding a number of bounds which enable the stability of the reconstruction problem to be predicted in advance, as well as the convergence rate of some of the iterations.