On the convergence of wavelet-based iterative signal extrapolation algorithms

A generalized Papoulis-Gerchberg (PG) algorithm for signal extrapolation based on the wavelet representation has been recently proposed by Xia, Kuo and Zhang. In this research, we examine the convergence property and the convergence rate of several signal extrapolation algorithms in wavelet subspaces. We first show that the generalized PG algorithm converges to the minimum norm solution when the wavelet bases are semi-orthogonal (or known as the prewavelet). However, the generalized PG algorithm converges slowly in numerical implementation. To accelerate the convergence rate, we formulate the discrete signal extrapolation problem as a two-step process and apply the steepest descent and conjugate gradient methods for its solution. Numerical experiments are given to illustrate the performance of the proposed algorithms.