Iterative time-limited signal restoration

This technical report deals with signal restoration and extrapolation. First, we prove that time-limited deconvolution and time-limited time-variant linear restoration of multidimensional signals can be done by means of fixed-point solutions of contraction mappings. Then, the band-limited multi-dimensional signal extrapolation problem is studied. (1) We provide several new algorithms for solving the discrete extrapolation problem and show the convergence of the discrete solutions so obtained to the continuous extrapolation. (2) We propose four basic models for the extrapolation problem and we present some new techniques for solving the continuous extrapolation problem when the known part of the signal is contaminated with noise. (3) Several results concerning iterative algorithms for band-limited extrapolation are presented.