Deconvolution of time series using wavelet transform - (Introduction of wavelet packets with soft-thresholding and generation of optimized wavelets)

A new discrete deconvolution procedure is developed that uses the wavelet p acket based system decompositon. The system is decomposed into subsystems u sing the wavelet packet transform and the inversion of each subsystem is de rived approximately. We show how to select the wavelet packet bases to miti gate the effects of illposedness due to the narrow bandwidth of the system. A new wavelet bases family with the optimal transition band performance is generated to surpress the approximation error. Furthermore we introduce th e soft thresholding into our procedure to reconstruct temporal inhomogeniou s signals more efficiently.