Smooth Biorthogonal Wavelets for Applications in Image Compression

IMAGE COMPRESSION Jan E. Odegard C. Sidney Burrus Department of Electrical and Computer Engineering Rice University, Houston, Texas 77005-1892, USA [email protected], [email protected] http: www-dsp.rice.edu ABSTRACT In this paper we introduce a new family of smooth, symmetric biorthogonal wavelet basis. The new wavelets are a generalization of the Cohen, Daubechies and Feauveau (CDF) biorthogonal wavelet systems. Smoothness is controlled independently in the analysis and synthesis bank and is achieved by optimization of the discrete finite variation (DFV) measure recently introduced for orthogonal wavelet design. The DFV measure dispenses with a measure of differentiability (for smoothness) which requires a large number of vanishing wavelet moments (e.g., Hölder and Sobolev exponents) in favor of a smoothness measure that uses the fact that only a finite depth of the filter bank tree is involved in most practical applications. Image compression examples applying the new filters using the embedded wavelet zerotree (EZW) compression algorithm due to Shapiro shows that the new basis functions performs better when compared to the classical CDF 7/9 wavelet basis.