Wavelet-based Signal Extrapolation

In this paper, we investigate the wavelet analogue of the well-known bandlimited extrapolation procedure of Papoulis and Gerchberg which replaces lost information from a bandlimited signal. The emphasis is on the discrete periodsed case. After a brief introduction to the notions of multiresolution analysis, wavelet subspaces and quadrature mirror filters, the associated periodised versions of these ideas are discussed. A method of mediating between sampled function values and sdmg function coefficients in the periodised case is gven. Criteria for solvability and an algorithmic solution with corresponding convergence results are stated and calculations made which verify these criteria in a number of examples. Finally, the algorithm is applied to several signals and images.