论文标题
在任意图上的光谱折叠和两道通道滤波器
Spectral folding and two-channel filter-banks on arbitrary graphs
论文作者
论文摘要
在过去的十年中，已经提出了几种用于图形信号的多分辨率表示理论。两部分过滤器银行是时域滤波器银行最自然的扩展，部分原因是图谱域中的完美重建，正交性和双交状况类似于传统的滤波器库。因此，许多众所周知的正交和双轴设计很容易适应图形信号。一个主要的限制是，该框架只能应用于二分图的归一化拉普拉斯。在本文中，我们将该理论扩展到任意图和正半准差异算子。我们的方法基于图形傅立叶变换（GFT）的不同定义，其中正交性与Q内产物的尊重定义。我们构建满足光谱折叠属性的GFT，这使我们能够轻松构建正交和双轴完美重建滤网。我们说明了我们的滤波器银行在3D点云上的信号表示和计算效率，数十万个点。
In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction, orthogonality and bi-orthogonality conditions in the graph spectral domain resemble those for traditional filter-banks. Therefore, many of the well known orthogonal and bi-orthogonal designs can be easily adapted for graph signals. A major limitation is that this framework can only be applied to the normalized Laplacian of bipartite graphs. In this paper we extend this theory to arbitrary graphs and positive semi-definite variation operators. Our approach is based on a different definition of the graph Fourier transform (GFT), where orthogonality is defined with the respect to the Q inner product. We construct GFTs satisfying a spectral folding property, which allows us to easily construct orthogonal and bi-orthogonal perfect reconstruction filter-banks. We illustrate signal representation and computational efficiency of our filter-banks on 3D point clouds with hundreds of thousands of points.
