Space-shift sampling of graph signals

A novel scheme for sampling graph signals is proposed. Space-shift sampling can be understood as a hybrid scheme that combines selection sampling -- observing the signal values on a subset of nodes - and aggregation sampling - observing the signal values at a single node after successive aggregation of local data. Under the assumption of bandlimitedness, we state conditions and propose strategies for signal recovery in different settings. Being a more general procedure, space-shift sampling achieves smaller reconstruction errors than current schemes, as we illustrate through the reconstruction of the industrial activity in a graph of the U.S. economy.

[1]  F. Pukelsheim.  Optimal Design of Experiments , 1993 .

[2]  Jelena Kovacevic,et al.  Discrete Signal Processing on Graphs: Sampling Theory , 2015, IEEE Transactions on Signal Processing.

[3]  Antonio Ortega,et al.  Towards a sampling theorem for signals on arbitrary graphs , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[4]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[5]  Michael G. Rabbat,et al.  Approximating signals supported on graphs , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[6]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Dustin G. Mixon,et al.  Full Spark Frames , 2011, 1110.3548.

[8]  Michael G. Rabbat,et al.  Graph spectral compressed sensing for sensor networks , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[9]  M. Unser.  Sampling-50 years after Shannon , 2000, Proceedings of the IEEE.

[10]  Ilan Shomorony,et al.  Sampling large data on graphs , 2014, 2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP).

[11]  Vincent Gripon,et al.  Towards a spectral characterization of signals supported on small-world networks , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[12]  José M. F. Moura,et al.  Discrete Signal Processing on Graphs , 2012, IEEE Transactions on Signal Processing.

[13]  Michael Jackson,et al.  Optimal Design of Experiments , 1994 .

[14]  Pascal Frossard,et al.  The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains , 2012, IEEE Signal Processing Magazine.

[15]  José M. F. Moura,et al.  Discrete Signal Processing on Graphs: Frequency Analysis , 2013, IEEE Transactions on Signal Processing.

[16]  Santiago Segarra,et al.  Sampling of graph signals: Successive local aggregations at a single node , 2015, 2015 49th Asilomar Conference on Signals, Systems and Computers.

[17]  Pengfei Liu,et al.  Local-Set-Based Graph Signal Reconstruction , 2014, IEEE Transactions on Signal Processing.

[18]  Santiago Segarra,et al.  Aggregation sampling of graph signals in the presence of noise , 2015, 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[19]  Michael Elad,et al.  Optimized Projections for Compressed Sensing , 2007, IEEE Transactions on Signal Processing.

[20]  Santiago Segarra,et al.  Sampling of Graph Signals With Successive Local Aggregations , 2015, IEEE Transactions on Signal Processing.