Enhanced B-spline based compression performance for images

The B-spline mathematical functions have long been utilized for signal representation, zooming and interpolation. However they have not been investigated for different image coding applications. In spite of the fact that B-splines are a semi-orthogonal basis (not full orthogonal) they still can be utilized for redundancy removal and decorrelation maximization prior to any compression scheme. This is due to their distinctive feature of preserving energy in low frequencies. In this paper we propose a novel technique for preprocessing signals/images prior to the decomposition stage in different image coders based on the B-spline decomposition. Mathematical explanation and derivation for the proposed B-spline decomposition basis is presented and analyzed. We derive our theoretic/mathematical justification, through some Eigen analysis calculations, for the enhancement in compression performance achieved with our B-spline based compression approach. We also present a straightforward approach for calculating the B-spline basis in a fast and efficient manner. Extensive simulations have been carried out on the well known SPIHT image coder with and without the proposed correlation removal methodology. Simulation results that demonstrate the effectiveness of the proposed technique are presented.