One-step-ahead kinematic compressive sensing

A large portion of work on compressive sampling and sensing has focused on reconstructions from a given measurement set. When the individual samples are expensive and optional, as is the case with autonomous agents operating in a physical domain and under specific energy limits, the CS problem takes on a new aspect because the projection is column-sparse, and the number of samples is not necessarily large. As a result, random sampling may no longer be the best tactic. The underlying incoherence properties in l0 reconstruction, however, can still motivate the purposeful design of samples in planning for CS with one or more agents; we develop here a greedy and computationally tractable sampling rule that will improve errors relative to random points. Several example cases illustrate that the approach is effective and robust.

[1]  Yiming Pi,et al.  Optimized ProjectionMatrix for Compressive Sensing , 2010 .

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

[3]  P.P. Vaidyanathan,et al.  Compressed sensing in MIMO radar , 2008, 2008 42nd Asilomar Conference on Signals, Systems and Computers.

[4]  Harald Haas,et al.  Asilomar Conference on Signals, Systems, and Computers , 2006 .

[5]  R. Castro,et al.  Tracking Hydrocarbon Plume Transport and Biodegradation at Deepwater Horizon , 2010 .

[6]  Richard M. Karp,et al.  Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane , 1977, Math. Oper. Res..

[7]  David M. Stein,et al.  An Asymptotic, Probabilistic Analysis of a Routing Problem , 1978, Math. Oper. Res..

[8]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[9]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[10]  Urbashi Mitra,et al.  Mission design for compressive sensing with mobile robots , 2011, 2011 IEEE International Conference on Robotics and Automation.

[11]  Howie Choset,et al.  Coverage for robotics – A survey of recent results , 2001, Annals of Mathematics and Artificial Intelligence.

[12]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.

[13]  Gaurav S. Sukhatme,et al.  Planning and Implementing Trajectories for Autonomous Underwater Vehicles to Track Evolving Ocean Processes Based on Predictions from a Regional Ocean Model , 2010, Int. J. Robotics Res..

[14]  S. LaValle,et al.  Randomized Kinodynamic Planning , 2001 .

[15]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[16]  Thomas Strohmer,et al.  Compressed sensing for MIMO radar - algorithms and performance , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[17]  D. Yoerger,et al.  Tracking Hydrocarbon Plume Transport and Biodegradation at Deepwater Horizon , 2010, Science.

[18]  H. Vincent Poor,et al.  Measurement Matrix Design for Compressive Sensing–Based MIMO Radar , 2011, IEEE Transactions on Signal Processing.

[19]  Guillermo Sapiro,et al.  Learning to Sense Sparse Signals: Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization , 2009, IEEE Transactions on Image Processing.