A parametrization technique to design joint time-frequency optimized discrete-time biorthogonal wavelet bases

The accurate and efficient representation of a signal in terms of elementary atoms has been a challenge in many signal processing applications including harmonic analysis. The wavelet bases have been proved to be very efficient and flexible atoms. Towards the goal of obtaining optimal wavelet bases, we present a simple and efficient parametrization technique for constructing linear phase biorthogonal discrete-time wavelet bases that have joint time-frequency localization (JTFL) close to the lower bound of 0.25. In this paper, we first develop a parametrization technique to design biorthogonal filter banks (FBs). Then an optimization method is formulated to design jointly time-frequency localized discrete wavelet bases employing the designed FBs. Finally, the performance of the optimal wavelet bases is evaluated in image coding application. The proposed parametrization method presents a general and yet a very simple framework to construct a linear phase biorthogonal FB of desired order, with the prescribed number of vanishing moments (VMs) and free parameters. Several examples are presented to demonstrate the effectiveness and flexibility of the technique to design different classes of FB with various degrees of freedom. The performance of the designed FBs is compared with the other popular biorthogonal wavelet FBs.