Department of Electrical Engineering, University of Colorado, Boulder, CO 80309-0425, USA.
IEEE Trans Image Process. 2000;9(5):792-800. doi: 10.1109/83.841526.
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 is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image. Emphasis is placed on developing algorithms that are computationally efficient. We developed a new fast two-dimensional (2-D) convolution decimation algorithm with factorized nonseparable 2-D filters. The algorithm is four 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 out performs one of the best wavelet coder on images such as Barbara and fingerprints, both visually and in term of PSNR.
强度的快速变化只能通过小尺度的小波系数来描述，这些系数往往被量化为零，即使在高比特率下也是如此。我们的目标是提供最佳小波包算法的快速数值实现，以证明通过构建适应目标图像的基可以获得优势。重点是开发计算效率高的算法。我们开发了一种新的快速二维（2-D）卷积抽取算法，具有可分解的非分离二维滤波器。该算法的速度比标准卷积抽取快四倍。该算法在一大类纹理图像上进行了广泛的评估。由于其能够很好地再现纹理的能力，小波包编码器在图像质量方面明显优于最佳的小波编码器之一，无论是在视觉上还是在 PSNR 方面，如 Barbara 和指纹图像。
