Deconvolution of Time Series Using Wavelet Transform : (Introduction of Wavelet Packets with Soft-Thresholding and Generation of Optimized Wavelets)

Abstract

A new discrete deconvolution procedure is developed that uses the wavelet packet based system decomposition.The system is decomposed into subsystems using the wavelet packet transform and the inversion of each subsystem is derived approx imately.We show how to select the wavelet packet bases to mitigate the effects of ill-posedness 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.Futhermore we introduce the soft thresholding into our procedure to reconstruct temporal inhomogenious signals more efficiently.