Signal Extrapolation in Wavelet Subspaces

The Papoulis–Gerchberg (PG) algorithm is well known for band-limited signal extrapolation. The authors consider the generalization of the PG algorithm to signals in the wavelet subspaces in this research. The uniqueness of the extrapolation for continuous-time signals is examined, and sufficient conditions on signals and wavelet bases for the generalized PG (GPG) algorithm to converge are given. A discrete GPG algorithm is proposed for discrete-time signal extrapolation, and its convergence is investigated. Numerical examples are given to illustrate the performance of the discrete GPG algorithm.

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