Optimization Design of Two-Channel Biorthogonal Graph Filter Banks
- 273 Downloads
Narang and Ortega have constructed a two-channel biorthogonal graph filter bank with compact support. The design method does not consider the spectral response of the kernels. In this letter, we employ optimization approach to design the spectral kernels. The analysis and synthesis kernels are, respectively, optimized with constrained optimization problems, in which the reconstruction error and spectral selectivity are controlled simultaneously. The optimization problems are semidefinite programming (SDP), which can be solved effectively. Numerical examples and comparison are included to show that the proposed approach is more flexible in making trade-off between the spectral selectivity and reconstruction error over the existing method.
KeywordsGraph filter bank Spectral kernel Optimization
The authors would like to thank Dr. Sunil K. Narang and Prof. Antonio Ortega for sharing MATLAB code of graph filter bank Online.
- 2.M. Crovella, E. Kolaczyk, Graph wavelets for spatial traffic analysis. IEEE INFOCOM 3, 1848–1857 (2003)Google Scholar
- 3.D.K. Hammod, P. Vandergheynst, R. Gribonval, Wavelets on graphs via spectral graph theory. Appl. Comput. Harmonic Anal. 30(2), 129–150 (2011)Google Scholar
- 5.S.K. Narang, A. Ortega, Lifting based wavelet transforms on graphs, in Proceedings Asia-Pacific Signal and Information Processing Association (2009), pp. 441–444Google Scholar
- 12.M.J. Wainwright, M.I. Jordan, Graphical Models, Exponential Families, and Variational Inference (Now Publishers, Hanover, 2008)Google Scholar
- 13.W. Wang, K. Ramchandran, Random multiresolution representations for arbitrary sensor network graphs, Proceedings International Conference on Acoustics, Speech and Signal Processing, vol. 4 (2006), pp. VI 161–164Google Scholar