An iterative algorithm for two-scale wavelet decomposition

This correspondence proposes an iterative method to decompose an arbitrary mother wavelet into a bandpass filter and a lowpass filter, where the filter pair will reproduce the mother wavelet through the two-scale equations. This problem is not straightforward because the two-scale relationship between the filter pair and the mother wavelet is nonlinear. The method finds the filter pair by minimizing an objective function with respect to one filter in an iteration and the other in the next iteration until convergence. The algorithm requires least-squares minimization only and is computationally efficient. The performance of the proposed algorithm is supported by simulations.