Hewlett-Packard Co., Palo Alto, CA.
IEEE Trans Image Process. 1997;6(9):1213-30. doi: 10.1109/83.623186.
We examine the question of how to choose a space varying filterbank tree representation that minimizes some additive cost function for an image. The idea is that for a particular cost function, e.g., energy compaction or quantization distortion, some tree structures perform better than others. While the wavelet tree represents a good choice for many signals, it is generally outperformed by the best tree from the library of wavelet packet frequency-selective trees. The double-tree library of bases performs better still, by allowing different wavelet packet trees over all binary spatial segments of the image. We build on this foundation and present efficient new pruning algorithms for both one- and two-dimensional (1-D and 2-D) trees that will find the best basis from a library that is many times larger than the library of the single-tree or double-tree algorithms. The augmentation of the library of bases overcomes the constrained nature of the spatial variation in the double-tree bases, and is a significant enhancement in practice. Use of these algorithms to select the least-cost expansion for images with a rate-distortion cost function gives a very effective signal adaptive compression scheme. This scheme is universal in the sense that, without assuming a model for the signal or making use of training data, it performs very well over a large class of signal types. In experiments it achieves compression rates that are competitive with the best training-based schemes.
我们研究了如何选择空间变化滤波器组树表示，以最小化图像的某些附加成本函数的问题。其思想是，对于特定的成本函数，例如能量紧缩或量化失真，某些树结构比其他结构表现更好。虽然对于许多信号来说，小波树是一个很好的选择，但它通常不如来自小波包频率选择树库中的最佳树表现好。双树库基的性能更好，允许在图像的所有二进制空间段上使用不同的小波包树。在此基础上，我们提出了一种高效的新算法，用于一维（1-D）和二维（2-D）树的修剪，该算法将从比单树或双树算法库大很多倍的库中找到最佳基。基库的扩充克服了双树基中空间变化的约束性质，在实践中是一个显著的增强。使用这些算法选择具有率失真成本函数的图像的最低成本扩展，可以得到一种非常有效的信号自适应压缩方案。这种方案是通用的，因为它不需要假设信号模型或使用训练数据，在很大一类信号类型上都能表现得非常好。在实验中，它实现了与最佳基于训练的方案相竞争的压缩率。
