Flexible tree-structured signal expansions using time-varying wavelet packets
Flexible tree-structured signal expansions using time-varying wavelet packets
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DOI：
10.1109/78.554299
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发表时间：
1997-02
期刊：
影响因子：
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通讯作者：
Zixiang Xiong;K. Ramchandran;Cormac Herley;M. Orchard
中科院分区：
文献类型：
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作者：
Zixiang Xiong;K. Ramchandran;Cormac Herley;M. Orchard
解决了为信号寻找最佳时变滤波器组树形结构表示的问题。允许树以规则的间隔变化，并且这些变化的间隔可以任意短。考虑了如何基于滤波器组选择信号的树形结构表示的问题。小波及其自适应版本，称为小波包，代表了一种流行的方法。小波包是子带树，其中树被选择来匹配信号的特征。在树随时间变化的情况下，已经提出了二叉树和时频树算法。时间变化增加了更高水平的适应性。在到目前为止提出的所有方法中，树必须在信号的整个持续时间内固定或在其二进制子间隔内固定。我们提出的解决方案，因为它允许更灵活的变化，是对小波包算法、双树算法和最近提出的时频树算法的改进。我们的解决方案是基于在动态编程(DP)设置中进行强制转换。针对压缩应用，我们使用拉格朗日失真代价+/SPLλ//SPL次数/速率作为目标函数，并详细解释了我们的算法，指出了它与现有方法的关系。我们证明了新算法确实比以前搜索到了更大的表示库，并且克服了二进制时间分割的限制，在实践中得到了显着的改进。
Addresses the problem of finding the best time-varying filter bank tree-structured representation for a signal. The tree is allowed to vary at regular intervals, and the spacing of these changes can be arbitrarily short. The question of how to choose tree-structured representations of signals based on filter banks is considered. Wavelets and their adaptive version, known as wavelet packets, represent one approach that is popular. Wavelet packets are subband trees where the tree is chosen to match the characteristics of the signal. Variations where the tree varies over time have been proposed as the double tree and the time-frequency tree algorithms. Time-variation adds a further level of adaptivity. In all of the approaches proposed so far, the tree must be either fixed for the whole duration of the signal or fixed for its dyadic subintervals. The solution that we propose, as it allows more flexible variation, is an advance on the wavelet packet algorithm, the double tree algorithm, and the recently proposed time-frequency tree algorithm. Our solution is based on casting it in a dynamic programming (DP) setting. Focusing on compression applications, we use a Lagrangian cost of distortion +/spl lambda//spl times/rate as the objective function and explain our algorithm in detail, pointing out its relation to existing approaches to the problem. We demonstrate that the new algorithm indeed searches a larger library of representations than previously possible and that overcoming the constraint of dyadic time segmentations gives a significant improvement in practice.