Iterative signal extrapolation algorithms with wavelets

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 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 os 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