Downsampling of signals on graphs via maximum spanning trees

IEEE Transactions on Signal Processing

Volumn 63, Issue 1, 2015, Pages 182-191

  Nguyen, Ha Q ^a,b   Do, Minh N ^a  

^a University of Illinois at Urbana Champaign   (United States)

^b EPFL   (Switzerland)

Author keywords

Bipartite approximation; Downsampling on graphs; Graph multiresolution; Graph wavelet filter banks; Max cut; Maximum spanning tree; Signal processing on graphs

Indexed keywords

FILTER BANKS; GRAPHIC METHODS; PARALLEL ARCHITECTURES; SIGNAL PROCESSING; SIGNAL SAMPLING; TELECOMMUNICATION NETWORKS; WAVELET TRANSFORMS; WEBSITES;

BIPARTITE APPROXIMATION; DOWNSAMPLING; GRAPH WAVELETS; MAX-CUT; MAXIMUM SPANNING TREE; MULTIRESOLUTION; SIGNAL PROCESSING ON GRAPHS;

TREES (MATHEMATICS);

EID: 84916918553     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2014.2369013     Document Type: Article

References (28)

1. D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega, and P. Vandergheynst, "The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains," IEEE Signal Process. Mag., vol. 30, no. 3, pp. 83-98, May 2013.
2. D. K. Hammond, P. Vandergheynst, and R. Gribonval, "Wavelets on graphs via spectral graph theory," Appl. Comput. Harmon. Anal., vol. 30, no. 2, pp. 129-150, Mar. 2011.
3. D. I. Shuman,M. J. Faraji, and P. Vandergheynst, "A Framework for Multiscale Transforms on Graphs," Aug. 2013 [Online]. Available: arXiv:1308.4942 [cs.IT]
4. S. K. Narang and A. Ortega, "Perfect reconstruction two-channel wavelet filter banks for graph structured data," IEEE Trans. Signal Process., vol. 60, no. 6, pp. 2786-2799, Jun. 2012.
5. S. K. Narang and A. Ortega, "Compact support biorthogonal wavelet filterbanks for arbitrary undirected graphs," IEEE Trans. Signal Process., vol. 61, no. 19, pp. 4673-4685, Oct. 1, 2013.
6. A. Sandryhaila and J. M. F. Moura, "Discrete signal processing on graphs," IEEE Trans. Signal Process., vol. 61, no. 7, pp. 1644-1656, Apr. 1, 2013.
7. H. Q. Nguyen, P. A. Chou, and Y. Chen, "Compression of human body sequences using graph wavelet transforms," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP 2014), May 2014, pp. 6152-6156.
8. R. M. Karp, "Reducibility among combinatorial problems," in Complexity of Computer Computations, R. E. Miller J. W. Thatcher, Ed. New York, NY, USA: Plenum Press, 1972, pp. 85-103.
9. W. Klotz, Graph Coloring Algorithms TU Clausthal, Tech, Rep. Mathematik-Bericht 2002/5, 2002.
10. D. Brélaz, "New methods to color the vertices of a graph," Commun. ACM, vol. 22, no. 4, pp. 251-256, Apr. 1979.
11. F. R. K. Chung, Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92). Providence, RI, USA: Amer. Math. Soc., 1997.
12. B. Aspvall and J. R. Gilbert, "Graph coloring using eigenvalue decomposition," SIAM J. Alg. Disc. Meth., vol. 5, no. 4, pp. 526-538, 1984.
13. I. Oren, "Nodal domain counts and the chromatic number of graphs," J. Phys. A: Math. Theor., vol. 40, no. 32, pp. 9825-9832, 2007.
14. F. Dörfler and F. Bullo, "Kron reduction of graphs with applications to electrical networks," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 60, no. 1, pp. 150-163, Jan. 2013.
15. D. A. Spielman and N. Srivastava, "Graph sparsification by effective resistances," SIAM J. Comput., vol. 40, no. 6, pp. 1913-1026, Dec. 2011.
16. R. C. Prim, "Shortest connection networks and some generalizations," Bell Syst. Tech. J., vol. 36, no. 6, pp. 1389-1401, Nov. 1957.
17. J. B. Kruskal, "On the shortest spanning subtree of a graph and the traveling salesman problem," Proc. Amer. Math. Soc., vol. 7, pp. 48-50, 1956.
18. M. Vetterli and J. Kovac¸ević, Wavelets and Subband Coding. Upper Saddle River, NJ, USA: Prentice Hall, 1995.
19. A. Cohen, I. Daubechies, and J.-C. Feauveau, "Biorthogonal bases of compactly supported wavelets," Commun. Pure Appl. Math., vol. 45, no. 5, pp. 485-560, Jun. 1992.
20. D. J. Klein and M. Randić, "Resistance distance," J. Math. Chem., vol. 12, no. 1, pp. 81-95, Dec. 1993.
21. S. K. Narang and A. Ortega, "Local two-channel critically sampled filter-banks on graphs," in Proc. 2010 IEEE Int. Conf. Image Process. (ICIP 2010), Sep. 2010, pp. 333-336.
22. M. J. Faraji, "A Laplacian pyramid scheme in graph signal processing," master's thesis, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, 2011.
23. P. Milanfar, "A tour of modern image filtering," IEEE Signal Process. Mag., vol. 30, no. 1, pp. 106-128, Jan. 2013.
24. B. Ricaud, D. I. Shuman, and P. Vandergheynst, "On the sparsity of wavelet coefficients for signals on graphs," in Proc. SPIE Wavelets Sparsity XV, Sep. 2013, pp. 1-7.
25. D. Gleich, MatlabBGL Oct. 2008 [Online]. Available: https://www.cs.purdue.edu/homes/dgleich/packages/matlab-bgl/
26. S. K. Narang, "GraphBior-Filterbanks," Nov. 2012 [Online]. Available: http://biron.usc.edu/kumarsun/Codes/graphBior-Filterbanks
27. P. Erdös and A. Rényi, "On random graphs, I," Publicationes Mathematicae (Debrecen), vol. 6, pp. 290-297, 1959.
28. J. Gall, C. Stoll, E. de Aguiar, C. Theobalt, B. Rosenhahn, and H.-P. Seidel, "Motion capture using joint skeleton tracking and surface estimation," in Proc. IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR'09), Jun. 2009, pp. 1746-1753.