论文标题
完美的重建两通道过滤器库在任意图上
Perfect Reconstruction Two-Channel Filter Banks on Arbitrary Graphs
论文作者
论文摘要
本文将现有的完美重建两通道滤波器库的现有理论从两部分图到非双分化图。通过概括下采样/上采样的概念，我们在任意连接，无方向性和加权图上建立了两通道滤波器库的框架。然后在适当的条件下呈现并解决了完美重建过滤库的方程式。给出了设计正交和生物三相库的算法，并计算了两个典型的正交两通道滤网。理论上和实验中讨论了此类滤清器库的局部性和近似特性。
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.
