The extended generalized Haar-Walsh transform and applications
The extended generalized Haar-Walsh transform and applications
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DOI：
10.1117/12.2528923
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
Y. Shao;N. Saito
中科院分区：
文献类型：
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作者：
Y. Shao;N. Saito
将计算调和分析工具从规则晶格的经典设置扩展到更一般的图和网络设置非常重要，并且最近已经进行了大量研究。我们之前的广义 Haar-Walsh 变换（GHWT）是图上信号的多尺度变换，它是经典 Haar 和 Walsh-Hadamard 变换的推广。本文提出了扩展的广义 HaarWalsh 变换（eGHWT）。 eGHWT 及其相关的图信号最佳基础选择算法将显着提高先前 GHWT 的性能，并且具有类似的计算成本 O(N log N)，其中 N 是输入图的节点数。之前的 GHWT/best-basis 算法会在超过 (1.5)N 个可能的碱基中寻找给定任务最合适的正交基，而 eGHWT/best-basis 算法可以通过搜索超过 0.618 · (1.84)N 个可能的碱基来找到更好的标准基。本文描述了 eGHWT/basis-basis 算法的详细信息，并使用几个示例展示了其优越性，包括真实的图形信号以及被视为图形信号的传统数字图像。
Extending computational harmonic analysis tools from the classical setting of regular lattices to the more general setting of graphs and networks is very important and much research has been done recently. Our previous Generalized Haar-Walsh Transform (GHWT) is a multiscale transform for signals on graphs, which is a generalization of the classical Haar and Walsh-Hadamard Transforms. This article proposes the extended Generalized HaarWalsh Transform (eGHWT). The eGHWT and its associated best-basis selection algorithm for graph signals will significantly improve the performance of the previous GHWT with the similar computational cost, O(N log N) where N is the number of nodes of an input graph. While the previous GHWT/best-basis algorithm seeks the most suitable orthonormal basis for a given task among more than (1.5)N possible bases, the eGHWT/best-basis algorithm can find a better one by searching through more than 0.618 · (1.84)N possible bases. This article describes the details of the eGHWT/basis-basis algorithm and demonstrates its superiority using several examples including genuine graph signals as well as conventional digital images viewed as graph signals.