Wavelets are ill suited to represent oscillatory patterns: rapid variations of intensity can only be described by the small scale wavelet coefficients. These diffused coefficients carry very little energy, and are often quantized to zero, even at high bit rates. Our goal in this paper is to provide a fast numerical implementation of the best wavelet packet algorithm [8] in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image. Emphasis in this paper has been placed on developing algorithms that are computationally efficient. We developed a new fast 2-D convolution-decimation algorithm with factorized non-separable 2-D filters. The algorithm is 4 times faster than a standard convolution-decimation. An extensive evaluation of the algorithm was performed on a large class of textured images. Because of its ability to reproduce textures so well, the wavelet packet coder significantly outperforms one of the best wavelet coder [26] on images such as Barbara, and Fingerprints, both visually and in term of PSNR.
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