Fast adaptive wavelet packet image compression

Wavelets are ill-suited to represent oscillatory patterns: rapid variations of intensity can only be described by the small scale wavelet coefficients , which are often quantized to zero, even at high bit rates. Our goal in th is paper is to provide a fast numerical implementation of the best wavelet packet algorithm [1] in order to demonstrate that an advantage can be gaine d by constructing a basis adapted to a target image. Emphasis in this paper has been placed on developing algorithms that are computationally efficien t. We developed a new fast two-dimensional (2-D) convolution-decimation alg orithm with factorized nonseparable 2-D filters. The algorithm is four time s faster than a standard convolution-decimation, An extensive evaluation of the algorithm was performed on a large class of textured images. Because o f its ability to reproduce textures so well, the wavelet packet coder signi ficantly out performs one of the best wavelet coder [2] on images such as B arbara and fingerprints, both visually and in term of PSNR.