论文标题
自然图小波包词典
Natural Graph Wavelet Packet Dictionaries
论文作者
论文摘要
我们通过在图形laplacian特征向量之间结合“自然”距离，而不是简单地使用特征值订购，从而引入了一组新型的多尺度基础转换，以利用其“双重”结构域的信号。这些基础词典可以看作是对任意图的经典香农小波包词典的概括，并且不依赖拉普拉斯特征值的频率解释。我们描述了算法（涉及向量旋转或正交化）来构建这些基本字典，使用它们通过最佳基础搜索有效地近似图形信号，并证明这些基础词典的强度，用于在葵花籽图和街道网络上测量的图形信号。
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.
