Spatial and frequency decomposition for image compression
Wei-Lien Hsu, Haluk Derin · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
This paper presents the design of an improved image compression algorithm based on an optimal spatial and frequency decomposition of images. The use of spatially varying wavelet packets for a generalized wavelet decomposition of images was recently introduced by Asai, Ramchandram and Vetterli. They use a `double tree' algorithm to obtain the optimal set of bases for a given image, through a joint optimization with respect to frequency decomposition by a wavelet packet and spatial decomposition based on a quad-tree structure. In this paper, we present a `double-tree' frequency and spatial decomposition algorithm that extends the existing algorithm in three areas. First, instead of the quad-tree structure, our algorithm uses a more flexible merging scheme for the spatial decomposition of the image. Second, instead of a scalar quantizer, we use a pyramidal lattice vector quantizer to represent each subband of each wavelet packet, which improves the coding efficiency of the representation. Both of these extensions yield an improved rate-distortion (R-D) performance. Finally, our algorithm uses a scheme that gives a good initial value for the slope of the R-D curve, reducing the total computations needed to obtain the optimum decompositions.