Bspline based Wavelets with Lifting Implementation

Abstract

The Bspline mathematical functions have long been utilized for signal representation. However they have been just recently been used for signal interpolation and zooming. Bsplines can represent the next generation of wavelets for signal/image compression and multi-resolution analysis. This is due to the fact that they are flexible and provide the best cost/quality trade off relationship. By changing the Bspline function order we move from a linear representation to a high order band limited representation. Bsplines are also linked to differentials, as they are the exact mathematical translators between the discrete and continuous versions of the coefficients. In this paper we propose a novel technique for signal/image decomposition, analysis, synthesis and reconstruction based on the Bspline mathematical functions. Mathematical explanation and derivation for the proposed Bspline prediction is analyzed. We also present a lifting based implementation for the proposed Bspline image coder and measure its effect on the compression quality. Extensive simulation results, which have been carried out with the proposed approach on different classes of images with different B-spline orders, are illustrated.