In this letter, we present a structure for two-channel spline graph filter bank with spectral sampling (SGFBSS) on arbitrary undirected graphs. Our proposed structure has many desirable properties; namely, perfect reconstruction, critical sampling in spectral domain, flexibility in the choice of shape and cut-off frequency of the filters, and low complexity implementation of the synthesis section, thanks to our closed-form derivation of the synthesis filter and its sparse structure. These properties play a pivotal role in multi-scale transforms of graph signals. Additionally, this framework can use both normalized and non-normalized Laplacian of any undirected graph. We evaluate the performance of our proposed SGFBSS structure in nonlinear approximation and denoising applications through simulations. We also compare our method with the existing graph filter bank structures and show its superior performance.

中文翻译：

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谱域样条图滤波器组

在这封信中，我们介绍了在任意无向图上具有频谱采样（SGFBSS）的两通道样条图滤波器组的结构。我们提出的结构具有许多理想的特性。也就是说，由于我们对合成滤波器及其稀疏结构进行了闭式推导，因此，完美的重构，频谱域中的关键采样，滤波器形状和截止频率选择的灵活性以及合成部分的低复杂度实现。这些特性在图形信号的多尺度转换中起着至关重要的作用。此外，此框架可以使用任何无向图的规范化和非规范化拉普拉斯算子。我们通过仿真评估了我们提出的SGFBSS结构在非线性逼近和降噪应用中的性能。