Tradeoffs in the design of wavelet filters for image compression
Patrice Onno, Christine M. Guillemot · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
This paper addresses the problem of joint optimization of wavelet transform, quantization, and data rate allocation according to mathematical criteria for high compression efficiency of image coding algorithms. The relevancy of some filter bank properties for compression purposes is evaluated. Using lattice structures, a large number of orthogonal and biorthogonal wavelet filter banks, with different properties of regularity, coding gain, phase linearity, and cross-correlation between adjacent bands are designed. Scalar and lattice vector quantization is then optimized adaptively to filter bank characteristics and to signal statistics. An appropriate choice of transition bandwidth, decreasing the energy around the Nyquist frequency without constraints of `zeros' in (omega) equals (pi) , provides by the maximum selectivity criterion filter banks close in performance to filters that we found optimum, and designed to satisfy either the maximum coding gain or minimum cross-correlation criterion. For a lower transition bandwidth, the increased regularity has for effect to increase the coding gain, to reach a maximum coding gain for maximally regular Daubechies filters. When comparing results of coding with the optimal orthogonal wavelet filter bank with those provided by a maximally frequency selective biorthogonal solution with same regularity it is observed that for a comparable peak SNR the contours are better reconstructed with biorthogonal solutions.