Design of Biorthogonal Wavelets based on Spline and Spline-like Functions for Image Compression

Abstract

Wavelet theory inspired from Fourier analysis is based on the basis function and its properties. Different wavelets use different basis functions which may better suit to some applications. The properties of basis functions along with their shape and magnification effects the performance of an application. The standard biorthogonal wavelets utilize spline functions for their construction. In this paper first the design procedure of biorthogonal wavelets is presented. Then a modified spline function is proposed. Based on the proposed spline function, three biorthogonal wavelets are designed with different length. The performance of proposed wavelets is analyzed by applying them on to images for SPIHT compression. The simulation results shown that the proposed wavelets have performed well compared to that of standard spline based biorthogonal wavelets.