Time Reversal and Cross Correlation Techniques for Inverse
Source Problems

Abdul Wahab
Department of Bio & Brain Engineering
Korea Advanced Institute of Science and Technology

Abstract. We present time reversal and cross correlation based mathematical techniques
to resolve inverse source problems, where the aim is to nd the spatial support of radiating
sources from boundary wave measurements. We rst deal with temporally localized acoustic,
elastic and electromagnetic sources and present time reversal algorithms for their resolution.
Then, we localize stationary Gaussian noise sources using cross-correlation based statistical
tools. Both spatially correlated and uncorrelated noise sources will be considered. For
correlated sources, we sketch a procedure for retrieving their correlation structure. The
eciency and robustness of the developed algorithms are substantiated through numerical
illustrations.
Joint work. This research has been jointly conducted with Prof. H. Ammari (ETH-Zurich),
Dr. E. Bretin (INSA-Lyon), Prof. J. Garnier (Paris VII), Prof. T. Hayat (QAU, Islamabad),
Dr. R. Nawaz (CIIT, Islamabad), and Dr. A. Rasheed (LUMS, Lahore).
References
[1] H. Ammari, E. Bretin, J. Garnier and A. Wahab, Time reversal in attenuating acoustic
media, in Mathematical and Statistical Methods for Imaging, Contemporary Mathematics,
vol. 548, AMS, (2011), 151{163.
[2] H. Ammari, E. Bretin, J. Garnier and A.Wahab, Time reversal algorithms in viscoeastic
media, European Journal of Applied Mathematics, 24(4):(2013), 565{600.
[3] H. Ammari, E. Bretin, J. Garnier and A.Wahab, Noise source localization in an attenuating
medium, SIAM Journal of Applied Mathematics, 72(1):(2012), 317{336.
[4] H. Ammari, E. Bretin, J. Garnier, H. Kang, and H. Lee and A.Wahab, Mathematical
Methods in Elasticity Imaging, Princeton Series in Applied Mathematics, Princeton
University Press, NJ, USA, 2015.
[5] A. Wahab, A. Rasheed, T. Hayat and R. Nawaz, Electromagnetic time reversal algorithms
and source localization in lossy dielectric media, Communications in Theoretical
Physics, 62(6):(2014), 779-789