Turbo Bayesian Compressed Sensing

Compressed sensing (CS) theory specifies a new signal acquisition approach, po- tentially allowing the acquisition of signals at a much lower data rate than the Nyquist sampling rate. In CS, the signal is not directly acquired but reconstructed from a few measurements. One of the key problems in CS is how to recover the original signal from measurements in the presence of noise. This dissertation addresses signal reconstruction problems in CS. First, a feedback structure and signal recovery algorithm, orthogonal pruning pursuit (OPP), is proposed to exploit the prior knowledge to reconstruct the signal in the noise-free situation. To handle the noise, a noise-aware signal reconstruction algorithm based on Bayesian Compressed Sensing (BCS) is developed. Moreover, a novel Turbo Bayesian Compressed Sensing (TBCS) algorithm is developed for joint signal reconstruction by exploiting both spatial and temporal redundancy. Then, the TBCS algorithm is applied to a UWB positioning system for achieving mm-accuracy with low sampling rate ADCs. Finally, hardware implementation of BCS signal reconstruction on FPGAs and GPUs is investigated. Implementation on GPUs and FPGAs of parallel Cholesky decomposition, which is a key component of BCS, is explored. Simulation results on software and hardware have demonstrated that OPP and TBCS outperform previous approaches, with UWB positioning accuracy improved by 12.8x. The accelerated computation helps enable real-time application of this work.

[1]  Richard G. Baraniuk,et al.  Bayesian Compressive Sensing Via Belief Propagation , 2008, IEEE Transactions on Signal Processing.

[2]  Dany Leviatan,et al.  Simultaneous approximation by greedy algorithms , 2006, Adv. Comput. Math..

[3]  G.R. Arce,et al.  Ultra-Wideband Compressed Sensing: Channel Estimation , 2007, IEEE Journal of Selected Topics in Signal Processing.

[4]  Joel A. Tropp,et al.  ALGORITHMS FOR SIMULTANEOUS SPARSE APPROXIMATION , 2006 .

[5]  Roman Wyrzykowski,et al.  Parallel Implementation of Cholesky LLT-Algorithm in FPGA-Based Processor , 2007, PPAM.

[6]  Bhaskar D. Rao,et al.  Sparse solutions to linear inverse problems with multiple measurement vectors , 2005, IEEE Transactions on Signal Processing.

[7]  Michael E. Tipping,et al.  Fast Marginal Likelihood Maximisation for Sparse Bayesian Models , 2003 .

[8]  Lawrence Carin,et al.  Bayesian Compressive Sensing , 2008, IEEE Transactions on Signal Processing.

[9]  Alexandros G. Dimakis,et al.  LP decoding meets LP decoding: A connection between channel coding and compressed sensing , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[10]  Aly E. Fathy,et al.  Millimeter accuracy UWB positioning system using sequential sub-sampler and time difference estimation algorithm , 2010, 2010 IEEE Radio and Wireless Symposium (RWS).

[11]  Chinmay Hegde,et al.  Compressive sensing of a superposition of pulses , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[12]  S. Kirolos,et al.  Analog-to-Information Conversion via Random Demodulation , 2006, 2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software.

[13]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[14]  Laura Rebollo-Neira,et al.  Backward-optimized orthogonal matching pursuit approach , 2004, IEEE Signal Processing Letters.

[15]  Aggelos K. Katsaggelos,et al.  Bayesian Compressive Sensing Using Laplace Priors , 2010, IEEE Transactions on Image Processing.

[16]  Volkan Cevher,et al.  Near-optimal Bayesian localization via incoherence and sparsity , 2009, 2009 International Conference on Information Processing in Sensor Networks.

[17]  M.R. Mahfouz,et al.  Real-Time Noncoherent UWB Positioning Radar With Millimeter Range Accuracy: Theory and Experiment , 2010, IEEE Transactions on Microwave Theory and Techniques.

[18]  Aly E. Fathy,et al.  UWB signal acquisition in positioning systems: Bayesian compressed sensing with redundancy , 2009, 2009 43rd Annual Conference on Information Sciences and Systems.

[19]  D. Pozar.  Microwave Engineering , 1990 .

[20]  Husheng Li,et al.  An FPGA Implementation for Solving Least Square Problem , 2009, 2009 17th IEEE Symposium on Field Programmable Custom Computing Machines.

[21]  J. Tropp.  Algorithms for simultaneous sparse approximation. Part II: Convex relaxation , 2006, Signal Process..

[22]  Dianne P. O'Leary,et al.  Cholesky decomposition and linear programming on a GPU , 2006 .

[23]  Wei Lu,et al.  Modified-CS: Modifying compressive sensing for problems with partially known support , 2009, 2009 IEEE International Symposium on Information Theory.

[24]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[25]  Husheng Li,et al.  High Performance Reconfigurable Computing for Cholesky Decomposition , 2009 .

[26]  Stephen J. Wright,et al.  Implementing Algorithms for Signal and Image Reconstruction on Graphical Processing Units , 2008 .

[27]  J. Haupt,et al.  A Generalized Restricted Isometry Property , 2008 .

[28]  Michael B. Wakin,et al.  Analysis of Orthogonal Matching Pursuit Using the Restricted Isometry Property , 2009, IEEE Transactions on Information Theory.

[29]  Philipp Birken,et al.  Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.

[30]  Joel A. Tropp,et al.  Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit , 2006, Signal Process..

[31]  Hui Wu,et al.  A reconfigurable, multi-gigahertz pulse shaping circuit based on distributed transversal filters , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[32]  Zhuizhuan Yu,et al.  Compressed UWB signal detection with narrowband interference mitigation , 2008, 2008 IEEE International Conference on Ultra-Wideband.

[33]  R. DeVore,et al.  A Simple Proof of the Restricted Isometry Property for Random Matrices , 2008 .

[34]  Mircea Andrecut,et al.  Fast GPU Implementation of Sparse Signal Recovery from Random Projections , 2008, Eng. Lett..

[35]  Justin Ziniel,et al.  Fast bayesian matching pursuit , 2008, 2008 Information Theory and Applications Workshop.

[36]  David B. Dunson,et al.  Multi-task compressive sensing with Dirichlet process priors , 2008, ICML '08.

[37]  Husheng Li,et al.  Decentralized Turbo Bayesian Compressed Sensing with Application to UWB Systems , 2011, EURASIP J. Adv. Signal Process..

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

[39]  Gregory Beylkin,et al.  Multiresolution quantum chemistry: basic theory and initial applications. , 2004, The Journal of chemical physics.

[40]  Husheng Li,et al.  Space-Time Turbo Bayesian Compressed Sensing for UWB Systems , 2010, 2010 IEEE International Conference on Communications.

[41]  Michael E. Tipping.  Sparse Bayesian Learning and the Relevance Vector Machine , 2001, J. Mach. Learn. Res..

[42]  W. S. Anglin,et al.  The heritage of Thales , 1995 .

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

[44]  Jerry Nedelman,et al.  Book review: “Bayesian Data Analysis,” Second Edition by A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin Chapman & Hall/CRC, 2004 , 2005, Comput. Stat..

[45]  Gregory D. Peterson,et al.  Performance Comparison of Cholesky Decomposition on GPUs and FPGAs , 2011 .

[46]  Yong Dou,et al.  64-bit floating-point FPGA matrix multiplication , 2005, FPGA '05.

[47]  Husheng Li,et al.  Feedback orthogonal pruning pursuit for pulse acquisition in UWB communications , 2009, 2009 IEEE 20th International Symposium on Personal, Indoor and Mobile Radio Communications.

[48]  Yazhou Wang,et al.  High accuracy UWB localization in dense indoor environments , 2008, 2008 IEEE International Conference on Ultra-Wideband.

[49]  Thong T. Do,et al.  Sparsity adaptive matching pursuit algorithm for practical compressed sensing , 2008, 2008 42nd Asilomar Conference on Signals, Systems and Computers.

[50]  Deanna Needell,et al.  Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit , 2007, IEEE Journal of Selected Topics in Signal Processing.

[51]  David B. Dunson,et al.  Multitask Compressive Sensing , 2009, IEEE Transactions on Signal Processing.

[52]  Wei Wang,et al.  Distributed Sparse Random Projections for Refinable Approximation , 2007, 2007 6th International Symposium on Information Processing in Sensor Networks.

[53]  Avi Septimus,et al.  Compressive sampling hardware reconstruction , 2010, Proceedings of 2010 IEEE International Symposium on Circuits and Systems.

[54]  Richard G. Baraniuk,et al.  An Information-Theoretic Approach to Distributed Compressed Sensing ∗ , 2005 .

[55]  Michael P. Friedlander,et al.  Theoretical and Empirical Results for Recovery From Multiple Measurements , 2009, IEEE Transactions on Information Theory.

[56]  David L. Donoho,et al.  Sparse Solution Of Underdetermined Linear Equations By Stagewise Orthogonal Matching Pursuit , 2006 .

[57]  Christian Jutten,et al.  Bayesian Pursuit algorithm for sparse representation , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[58]  Fan Zhang,et al.  On the Iterative Decoding of High-Rate LDPC Codes With Applications in Compressed Sensing , 2009, ArXiv.

[59]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

[60]  James Demmel,et al.  LU, QR and Cholesky Factorizations using Vector Capabilities of GPUs , 2008 .

[61]  Aly E. Fathy,et al.  Compressed sensing based UWB receiver: Hardware compressing and FPGA reconstruction , 2009, 2009 43rd Annual Conference on Information Sciences and Systems.