Optimal wavelet tree pruning for image coding
Yew Hock Ang, M. Bi, Sim Heng Ong · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
ABSTRACT In this paper, an optimal image coding scheme based on Waveletdecomposition and vector quantization is proposed. Theselection of wavelet transformed coefficients for encoding isperformed using an optimal Uee-pruning algorithm. Optimumselection of wavelet coefficients is achieved by minimizing the overallresidual quantization error of the pruned iree. Theprun-ing process takes into consideration the image structure and exploits thespatial masking effect of the human visual system. Thisreduces the overall coding bit rate without scarifying theperceptual quality in the reconstructed image. Vector quantization ofthe selected wavelet coefficients (pruned-tree) is performedusing our proposed multiresolution product codebook. The optimaldesign of the product codebook is characterized by its minimized andequally distributed quantization distortions of individualsub-codebooks.Keywords: wavelet tree pruning, wavelet coding, multiresolution codebook,product codebook 1. INTRODUCTION The wavelet transform is a well known method for muliiresolurjonrepresentation of image signals and is well salted forimage coding for two reasons; its is highly efficient in terms of spectraldecomposition and spatial localization of edge-featuresproperties. The first property allows image data to be decomposed into multiresolutionof sub-images or subbands of differentspectral components. The higher spectral sub-images typically contains lessenergy and therefore they can be discarded or codedat much reduced bit rates to achieve high image compression. The secondproperty allows more efficient assignment of codingbit resources to local edge features which are moreperceptually sensitive to the human visual system, and therefore maintainingits reconstruction qualityThere have been some promising results recently reported on theapplication of wavelet transform in image compression [1]-[7]. Recently, Antonini et al. [2], and Lewis and Knowles [3]separately proposed bit allocation schemes for image coding in thewavelet transform domain. The former proposed a product vectorquantization scheme based on the Gaussian sourceassump-tion, while the latter proposed a hierarchical quantization scheme basedon a fixed threshold on the wavelet transformed coeffi-cients. Both of these schemes do not take into consideration theperformance characteristics of the practical quantizer, and thealiasing effect of subband truncation on the reconstructed imagequality In this paper, we shown that improved coding effi-.ciency can be achieved by optimizing the allocation of bit resources to variouswavelet subbands, and ensuring the perceptuallymore important image details are preserved in the reconstruction. This two-foldobjective is achieved with our design of an opti-mal multresolution codebook and tree-pruning algorithm for waveletcoefficient selection.The pruning algorithm systematically allocate bit resourcesto the wavelet decomposed tree starting from the lowest to thehighest spectral subbands. This results in less aliasing effects from subbandtruncation and improved perceptual reconstruction