Compressive Sensing Meets Noise Radar

In this chapter, we discuss how noise radar systems are suitable for realizing practically the promises of compressive sensing in radar imaging, in general, and in urban-sensing applications, in particular. Noise radar refers to radio frequency imaging systems that employ transmit signals that are generated to resemble random noise waveforms. Noise radar has recently been successfully applied to urban sensing applications such as through-the-wall sensing (Amin 2011). Recent advances in the field of compressive sensing provide us with techniques to overcome the challenges of waveform design, sampling, and bandwidth constraints. We review existing literature related to these problems and present new results that enable

[1]  B. M. Horton.  Noise-Modulated Distance Measuring Systems , 1959, Proceedings of the IRE.

[2]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .

[3]  Douglas L. Jones,et al.  An adaptive optimal-kernel time-frequency representation , 1995, IEEE Trans. Signal Process..

[4]  P.R. Chakravarthi,et al.  On determining the radar threshold for non-Gaussian processes from experimental data , 1996, IEEE Trans. Inf. Theory.

[5]  Jinwen Li,et al.  The design of digital radar receivers , 1997, Proceedings of the 1997 IEEE National Radar Conference.

[6]  Ram M. Narayanan,et al.  Design, performance, and applications of a coherent ultra-wideband random noise radar , 1998 .

[7]  V. Chen,et al.  ISAR motion compensation via adaptive joint time-frequency technique , 1998 .

[8]  Alan V. Oppenheim,et al.  Discrete-time signal processing (2nd ed.) , 1999 .

[9]  Norman C. Beaulieu,et al.  A comparison of SNR estimation techniques for the AWGN channel , 2000, IEEE Trans. Commun..

[10]  A. Belouchrani,et al.  The spatial ambiguity function and its applications , 2000, IEEE Signal Processing Letters.

[11]  LJubisa Stankovic,et al.  A measure of some time-frequency distributions concentration , 2001, Signal Process..

[12]  Igor Djurovic,et al.  Robust L-estimation based forms of signal transforms and time-frequency representations , 2003, IEEE Trans. Signal Process..

[13]  T. Sparr,et al.  Micro-Doppler analysis of vibrating targets in SAR , 2003 .

[14]  Fabrice Labeau,et al.  Discrete Time Signal Processing , 2004 .

[15]  Andrzej Tarczynski,et al.  Spectral analysis of randomly sampled signals: suppression of aliasing and sampler jitter , 2004, IEEE Transactions on Signal Processing.

[16]  F. Berizzi,et al.  Time windowing for highly focused ISAR image reconstruction , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[17]  Mark A. Richards,et al.  Fundamentals of Radar Signal Processing , 2005 .

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

[19]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[20]  T. Thayaparan,et al.  Separation of target rigid body and micro-doppler effects in ISAR imaging , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[21]  R. Baraniuk,et al.  Compressive Radar Imaging , 2007, 2007 IEEE Radar Conference.

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

[23]  Moeness G. Amin,et al.  Compressed sensing technique for high-resolution radar imaging , 2008, SPIE Defense + Commercial Sensing.

[24]  Richard G. Baraniuk,et al.  Compressive Sensing , 2008, Computer Vision, A Reference Guide.

[25]  Ram M. Narayanan.  Through wall radar imaging using UWB noise waveforms , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[26]  M. Martorella,et al.  Novel approach for ISAR image cross-range scaling , 2008, IEEE Transactions on Aerospace and Electronic Systems.

[27]  Michael P. Friedlander,et al.  Probing the Pareto Frontier for Basis Pursuit Solutions , 2008, SIAM J. Sci. Comput..

[28]  Justin K. Romberg,et al.  Compressive Sensing by Random Convolution , 2009, SIAM J. Imaging Sci..

[29]  Thomas Strohmer,et al.  High-Resolution Radar via Compressed Sensing , 2008, IEEE Transactions on Signal Processing.

[30]  Andrea Montanari,et al.  Message-passing algorithms for compressed sensing , 2009, Proceedings of the National Academy of Sciences.

[31]  Bijan G. Mobasseri,et al.  A time-frequency classifier for human gait recognition , 2009, Defense + Commercial Sensing.

[32]  Cornel Ioana,et al.  Effects of Cauchy Integral Formula Discretization on the Precision of IF Estimation: Unified Approach to Complex-Lag Distribution and its Counterpart L-Form , 2009, IEEE Signal Processing Letters.

[33]  Emanuel Radoi,et al.  Superresolution algorithms for spatial extended scattering centers , 2009, Digit. Signal Process..

[34]  Ali Cafer Gürbüz,et al.  A Compressive Sensing Data Acquisition and Imaging Method for Stepped Frequency GPRs , 2009, IEEE Transactions on Signal Processing.

[35]  Ram M. Narayanan,et al.  Compressive radar imaging using white stochastic waveforms , 2010, 2010 International Waveform Diversity and Design Conference.

[36]  Joachim H. G. Ender,et al.  On compressive sensing applied to radar , 2010, Signal Process..

[37]  Andriyan Bayu Suksmono,et al.  Compressive Stepped-Frequency Continuous-Wave Ground-Penetrating Radar , 2010, IEEE Geoscience and Remote Sensing Letters.

[38]  Abdesselam Bouzerdoum,et al.  A Human Gait Classification Method Based on Radar Doppler Spectrograms , 2010, EURASIP J. Adv. Signal Process..

[39]  Richard G. Baraniuk,et al.  Signal Processing With Compressive Measurements , 2010, IEEE Journal of Selected Topics in Signal Processing.

[40]  Andrea Montanari,et al.  The dynamics of message passing on dense graphs, with applications to compressed sensing , 2010, 2010 IEEE International Symposium on Information Theory.

[41]  Stephen J. Wright,et al.  Computational Methods for Sparse Solution of Linear Inverse Problems , 2010, Proceedings of the IEEE.

[42]  Rama Chellappa,et al.  Adaptive Threshold Estimation via Extreme Value Theory , 2010, IEEE Transactions on Signal Processing.

[43]  Patrick Flandrin,et al.  Time-Frequency Energy Distributions Meet Compressed Sensing , 2010, IEEE Transactions on Signal Processing.

[44]  Moeness G. Amin,et al.  Through-the-Wall Radar Imaging using compressive sensing along temporal frequency domain , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[45]  Justin K. Romberg,et al.  Restricted Isometries for Partial Random Circulant Matrices , 2010, ArXiv.

[46]  Petre Stoica,et al.  Spectral analysis of nonuniformly sampled data - a review , 2010, Digit. Signal Process..

[47]  Robert D. Nowak,et al.  Toeplitz Compressed Sensing Matrices With Applications to Sparse Channel Estimation , 2010, IEEE Transactions on Information Theory.

[48]  Bengt E. Jonsson.  A survey of A/D-Converter performance evolution , 2010, 2010 17th IEEE International Conference on Electronics, Circuits and Systems.

[49]  A. Zoubir,et al.  Through-the-Wall Radar Imaging , 2010 .

[50]  Irena Orovic,et al.  A new approach for classification of human gait based on time-frequency feature representations , 2011, Signal Process..

[51]  Yonina C. Eldar,et al.  Xampling: Analog to digital at sub-Nyquist rates , 2009, IET Circuits Devices Syst..

[52]  Boualem Boashash,et al.  An Efficient Algorithm for Instantaneous Frequency Estimation of Nonstationary Multicomponent Signals in Low SNR , 2011, EURASIP J. Adv. Signal Process..

[53]  Jinghui Liu,et al.  A nonmonotone trust region method with new inexact line search for unconstrained optimization , 2012, Numerical Algorithms.

[54]  Irena Orovic,et al.  Compressed sensing based robust time-frequency representation for signals in heavy-tailed noise , 2012, 2012 11th International Conference on Information Science, Signal Processing and their Applications (ISSPA).

[55]  Tom Chau,et al.  Compressive sampling of swallowing accelerometry signals using time-frequency dictionaries based on modulated discrete prolate spheroidal sequences , 2012, EURASIP J. Adv. Signal Process..

[56]  Ram M. Narayanan,et al.  A Portable Real-Time Digital Noise Radar System for Through-the-Wall Imaging , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[57]  Ram M. Narayanan,et al.  Analysis and design of algorithms for compressive sensing based noise radar systems , 2012, 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[58]  Ming Gu,et al.  ParNes: a rapidly convergent algorithm for accurate recovery of sparse and approximately sparse signals , 2009, Numerical Algorithms.

[59]  Yimin Zhang,et al.  Compressive sensing in nonstationary array processing using bilinear transforms , 2012, 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[60]  Irena Orović,et al.  Compressive sensing for sparse time-frequency representation of nonstationary signals in the presence of impulsive noise , 2013, Defense, Security, and Sensing.

[61]  Irena Orovic,et al.  Compressive Sensing Based Separation of Nonstationary and Stationary Signals Overlapping in Time-Frequency , 2013, IEEE Transactions on Signal Processing.

[62]  Moeness G. Amin,et al.  Through-the-Wall Human Motion Indication Using Sparsity-Driven Change Detection , 2013, IEEE Transactions on Geoscience and Remote Sensing.

[63]  Ram M. Narayanan,et al.  Characterizing detection thresholds using extreme value theory in compressive noise radar imaging , 2013, Defense, Security, and Sensing.

[64]  Ram M. Narayanan,et al.  Waveform design for compressively sampled ultrawideband radar , 2013, J. Electronic Imaging.

[65]  Richard G. Baraniuk,et al.  Design and Analysis of Compressive Sensing Radar Detectors , 2012 .

[66]  Irena Orovic,et al.  Robust Time-Frequency Analysis Based on the L-Estimation and Compressive Sensing , 2013, IEEE Signal Processing Letters.

[67]  Irena Orovic,et al.  L-statistics based modification of reconstruction algorithms for compressive sensing in the presence of impulse noise , 2013, Signal Process..

[68]  Braham Himed,et al.  Reduced interference time-frequency representations and sparse reconstruction of undersampled data , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[69]  Moeness Amin,et al.  Instantaneous frequency and time-frequency signature estimation using compressive sensing , 2013, Defense, Security, and Sensing.

[70]  Yonina C. Eldar,et al.  Sub-Nyquist Radar via Doppler Focusing , 2012, IEEE Transactions on Signal Processing.

[71]  Srdjan Stankovic,et al.  Missing samples analysis in signals for applications to L-estimation and compressive sensing , 2014, Signal Process..

[72]  Moeness G. Amin,et al.  Compressive sensing for urban radar , 2014 .

[73]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[74]  Ram M. Narayanan,et al.  Conventional and emerging waveforms for detection and imaging of targets behind walls , 2017 .