论文标题
在任意图上具有完美重建的样条状小波过滤库
Spline-Like Wavelet Filterbanks with Perfect Reconstruction on Arbitrary Graphs
论文作者
论文摘要
在这项工作中，我们为图形信号提出了一类类似于样条的小波滤网。这些过滤库具有关键采样和完美重建的特性。此外，分析过滤器位于图域中，因为它们是图形标准化邻接矩阵的多项式。我们在文献中概括了类似样条的过滤器，以便它们能够消灭某些指定频率的信号。对于分析过滤器提出了优化问题，以近似所需的响应。我们进行了一些实验，以证明所提出的过滤器的良好位置以及在DeNoising任务中滤清器的良好性能。
In this work, we propose a class of spline-like wavelet filterbanks for graph signals. These filterbanks possess the properties of critical sampling and perfect reconstruction. Besides, the analysis filters are localized in the graph domain because they are polynomials of the normalized adjacency matrix of the graph. We generalize the spline-like filters in the literature so that they have the ability to annihilate signals of some specified frequencies. Optimization problems are posed for the analysis filters to approximate desired responses. We conduct some experiments to demonstrate the good locality of the proposed filters and the good performance of the filterbank in the denoising task.
