论文标题
基于优化模型，在任意图上的完美重建两通道滤波器库
Perfect Reconstruction Two-Channel Filter Banks on Arbitrary Graphs Based on an Optimization Model
论文作者
论文摘要
In this paper, we propose the construction of critically sampled perfect reconstruction two-channel filterbanks on arbitrary undirected graphs.Inspired by the design of graphQMF proposed in the literature, we propose a general ``spectral folding property'' similar to that of bipartite graphs and provide sufficient conditions for constructing perfect reconstruction filterbanks based on a general graph Fourier basis, which is not the eigenvectors Laplacian矩阵。为了获得所需的图傅立叶基础，我们需要解决一系列二次相等性约束的二次优化问题（QECQPS），这些问题已知是非凸面且难以解决的。我们开发了一种算法以在预先指定的公差内获得全局最佳解决方案。对现实数据和合成数据进行多分辨率分析，以验证所提出的滤纸的有效性。
In this paper, we propose the construction of critically sampled perfect reconstruction two-channel filterbanks on arbitrary undirected graphs.Inspired by the design of graphQMF proposed in the literature, we propose a general ``spectral folding property'' similar to that of bipartite graphs and provide sufficient conditions for constructing perfect reconstruction filterbanks based on a general graph Fourier basis, which is not the eigenvectors of the Laplacian matrix. To obtain the desired graph Fourier basis, we need to solve a series of quadratic equality constrained quadratic optimization problems (QECQPs) which are known to be non-convex and difficult to solve. We develop an algorithm to obtain the global optimal solution within a pre-specified tolerance. Multi-resolution analysis on real-world data and synthetic data are performed to validate the effectiveness of the proposed filterbanks.
