Extrapolation of Wideband Electromagnetic Response Using Sparse Representation

Wideband electromagnetic response can be extrapolated using combined low frequency and early time information, which can substantially reduce the computational load. Most existing extrapolation methods are based on orthogonal polynomials, but selecting optimal parameters of orthogonal polynomials is not straightforward. This work proposes to extrapolate wideband electromagnetic response using sparse representation. The electromagnetic response is expressed as linear combination of atoms from an overcomplete dictionary. Optimal linear combination of atoms is then sought through the affine scaling transformation and the support vector regression. By increasing the data length step by step, convergence of the sparse solution is used as a criterion to determine the sufficient data length. Performance analysis shows that our proposed extrapolation method retains lower computational complexity and renders more flexibility in reconstructing a signal. Numerical examples are presented to show the efficacy and advantages of the proposed extrapolation method.

[1]  Dmitry M. Malioutov,et al.  A sparse signal reconstruction perspective for source localization with sensor arrays , 2005, IEEE Transactions on Signal Processing.

[2]  Jinhwan Koh,et al.  A comparison of performance of three orthogonal polynomials in extraction of wide-band response using early time and low frequency data , 2005, IEEE Transactions on Antennas and Propagation.

[3]  M. S. Palma,et al.  Analysis of electromagnetic systems irradiated by ultra-short ultra-wideband pulse , 2001 .

[4]  Jinhwan Koh,et al.  Conditions for generation of stable and accurate hybrid TD-FD MoM solutions , 2006, IEEE Transactions on Microwave Theory and Techniques.

[5]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[6]  J. M. Frye,et al.  Extrapolation of Time and Frequency Responses of Resonant Antennas Using Damped Sinusoids and Orthogonal Polynomials , 2008, IEEE Transactions on Antennas and Propagation.

[7]  Ying Zhang,et al.  A partially sparse solution to the problem of parameter estimation of CARD model , 2008, Signal Process..

[8]  K. Kreutz-Delgado,et al.  Application of concave/Schur-concave functions to the learning of overcomplete dictionaries and sparse representations , 1998, Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284).

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

[10]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[11]  R. Demirli,et al.  Denoising and compression of ultrasonic signals using model-based estimation techniques , 2004, IEEE Ultrasonics Symposium, 2004.

[12]  Raviraj S. Adve,et al.  Simultaneous extrapolation in time and frequency domains using hermite expansions , 1999 .

[13]  Bhaskar D. Rao,et al.  Affine scaling transformation based methods for computing low complexity sparse solutions , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

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

[15]  Yunqian Ma,et al.  Selection of Meta-parameters for Support Vector Regression , 2002, ICANN.

[16]  Terrence J. Sejnowski,et al.  Blind source separation of more sources than mixtures using overcomplete representations , 1999, IEEE Signal Processing Letters.

[17]  Jean-Jacques Fuchs,et al.  Recovery of exact sparse representations in the presence of bounded noise , 2005, IEEE Transactions on Information Theory.

[18]  Bhaskar D. Rao,et al.  Bayesian learning for sparse signal reconstruction , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[19]  L. Vielva,et al.  A fast blind SIMO channel identification algorithm for sparse sources , 2003, IEEE Signal Processing Letters.

[20]  Brendt Wohlberg,et al.  Noise sensitivity of sparse signal representations: reconstruction error bounds for the inverse problem , 2003, IEEE Trans. Signal Process..

[21]  M.A. Jensen,et al.  Sparse Power Angle Spectrum Estimation , 2009, IEEE Transactions on Antennas and Propagation.

[22]  Bhaskar D. Rao,et al.  Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm , 1997, IEEE Trans. Signal Process..

[23]  D. Basak,et al.  Support Vector Regression , 2008 .

[24]  D. Donoho,et al.  Basis pursuit , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[25]  J. M. Frye,et al.  Time and Frequency Bias in Extrapolating Wideband Responses of Resonant Structures , 2009, IEEE Transactions on Antennas and Propagation.