自然图小波包字典
Natural Graph Wavelet Packet Dictionaries
摘要：
我们引入了一组新的多尺度基变换的信号图，利用其“双”域，将“自然”的距离图拉普拉斯特征向量，而不是简单地使用的特征值排序。这些基字典可以被看作是经典Shannon小波包字典到任意图的推广，并且不依赖于拉普拉斯特征值的频率解释。我们描述的算法（涉及向量旋转或正交化），以构建这些基础字典，使用它们来有效地近似图形信号，通过最佳的基础搜索，并证明这些基础字典的强度，向日葵图和街道网络上测量的图形信号。
英文摘要：
We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their "dual" domains by incorporating the "natural" distances between graph Laplacian eigenvectors, rather than simply using the eigenvalue ordering. These basis dictionaries can be seen as generalizations of the classical Shannon wavelet packet dictionary to arbitrary graphs, and do not rely on the frequency interpretation of Laplacian eigenvalues. We describe the algorithms (involving either vector rotations or orthogonalizations) to construct these basis dictionaries, use them to efficiently approximate graph signals through the best basis search, and demonstrate the strengths of these basis dictionaries for graph signals measured on sunflower graphs and street networks.
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