Optimal design of high-performance separable wavelet filter banks for image coding

An optimization-based method is proposed for the design of high-performance separable wavelet filter banks for image coding. This method yields linear-phase perfect-reconstruction systems with high coding gain, good frequency selectivity, and certain prescribed vanishing-moment properties. Several filter banks designed with the proposed method are presented and shown to work extremely well for image coding, outperforming the well-known 9/7 filter bank from JPEG 2000 in most cases. With the proposed design method, the coding gain can be maximized with respect to the separable or isotropic image model, or jointly with respect to both models. The joint case, which is shown to be equivalent to the isotropic case, is experimentally demonstrated to lead to filter banks with better average coding performance than the separable case. During the development of the proposed design method, filter banks from a certain popular separable 2D wavelet class (to which our optimal designs belong) were observed to always have a higher coding gain with respect to the separable image model than with respect to the isotropic one. This behavior is examined in detail, leading to the conclusion that, for filter banks belonging to the above class, it is highly improbable (if not impossible) for the isotropic coding gain to exceed the separable coding gain.