| Paper ID | SPTM-5.2 |
| Paper Title |
Spectral folding and two-channel filter-banks on arbitrary graphs |
| Authors |
Eduardo Pavez, University of Southern California, United States; Benjamin Girault, Université de Rennes, France; Antonio Ortega, University of Southern California, United States; Philip A. Chou, Google Research, United States |
| Session | SPTM-5: Sampling, Multirate Signal Processing and Digital Signal Processing 1 |
| Location | Gather.Town |
| Session Time: | Tuesday, 08 June, 16:30 - 17:15 |
| Presentation Time: | Tuesday, 08 June, 16:30 - 17:15 |
| Presentation |
Poster
|
| Topic |
Signal Processing Theory and Methods: [SMDSP] Sampling, Multirate Signal Processing and Digital Signal Processing |
| IEEE Xplore Open Preview |
Click here to view in IEEE Xplore |
| Virtual Presentation |
Click here to watch in the Virtual Conference |
| Abstract |
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 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. |
