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Time reversal imaging for sensor networks with optimal compensation in time
J. Acoust. Soc. Am. Volume 121, Issue 4, pp. 2071-2085 (2007); (15 pages)
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Add to FacebookUsing extensive numerical simulations, several distributed sensor imaging algorithms for localized damage in a structure are analyzed. Given a configuration of ultrasonic transducers, a full response matrix for the healthy structure is assumed known. It is used as a basis for comparison with the response matrix that is recorded when there is damage. Numerical simulations are done with the wave equation in two dimensions. The healthy structure contains many scatterers. The aim is to image point-like defects with several regularly distributed sensors. Because of the complexity of the environment, the recorded traces have a lot of delay spread and travel time migration does not work so well. Instead, the traces are back propagated numerically assuming that there is some knowledge of the background. Since the time at which the back propagated field will focus on the defects is unknown, the Shannon entropy or the bounded variation norm of the image is computed and the time where it is minimal is picked. This imaging method performs well because it produces a tight image near the location of the defects at the time of refocusing. When there are several defects, the singular value decomposition of the response matrix is also carried out.
© 2007 Acoustical Society of America
ACKNOWLEDGMENTS
The work of G. Derveaux, G. Papanicolaou, and C. Tsogka was partially supported by the Office of Naval Research N00014-02-1-0088, by the National Science Foundation DMS-0354674-001 and CMS-0451213, and by DARPA/ARO 02-SC-ARO-1067-MOD 1.
Article Outline
- INTRODUCTION
- DISTRIBUTED SENSOR FRAMEWORK FOR NUMERICAL SIMULATIONS
- TRAVEL TIME IMAGING
- TIME REVERSAL WITH OPTIMAL STOPPING
- Physical time reversal
- Numerical time reversal for imaging
- Shannon entropy
- BV norm
- Time reversal imaging with optimal stopping
- Results of numerical simulations
- Separation of the defects by singular value decomposition
- SVD of the response matrix in the frequency domain
- Imaging the defects using the traces projected on each singular vector
- Cumulative images
- IMAGING OF AN EXTENDED DEFECT
- SUMMARY AND CONCLUSIONS
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History
Received 04 Jul 2006
Accepted 11 Jan 2007
Revised 13 Nov 2006
Accepted 11 Jan 2007
Revised 13 Nov 2006
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