This paper extends the existing theory of perfect reconstruction two-channel filter banks from bipartite graphs to non-bipartite graphs. By generalizing the concept of downsampling/upsampling we establish the frame of two-channel filter bank on arbitrary connected, undirected and weighted graphs. Then the equations for perfect reconstruction of the filter banks are presented and solved under proper conditions. Algorithms for designing orthogonal and biorthogonal banks are given and two typical orthogonal two-channel filter banks are calculated. The locality and approximation properties of such filter banks are discussed theoretically and experimentally.

翻译：本文将从二分图上的完美重构两通道滤波器组理论推广至非二分图。通过推广下采样/上采样的概念，我们在任意连通无向加权图上建立了双通道滤波器组的框架。随后给出了滤波器组完美重构的方程，并针对适当条件进行求解。本文提出了正交与双正交滤波器组的设计算法，并计算了两种典型的正交双通道滤波器组。最后从理论与实验两方面探讨了此类滤波器组的局部性与逼近性质。