Time and direction of arrival detection and filtering for imaging in strongly scattering random media

Abstract

We study detection and imaging of small reflectors in heavy clutter, using an array of transducers that emits and receives sound waves. Heavy clutter means that multiple scattering of the waves in the heterogeneous host medium is strong and overwhelms the arrivals from the small reflectors. Building on the adaptive time-frequency filter of [Borcea et al, SIIMS 2011;4(3)], we propose a robust method for detecting the direction of arrival of the direct echoes from the small reflectors, and suppressing the unwanted clutter backscatter. This improves the resolution of imaging. We illustrate the performance of the method with realistic numerical simulations in a non-destructive testing setup.

Keywords:

• Array imaging
• random media
• time-frequency analysis
• direction of arrival
• data filtering

Acknowledgements

The work of L. Borcea was partially supported by a NAKFI Imaging Science award. Support from NSF grant DMS-1510429 is also gratefully acknowledged. The work of G. Papanicolaou was partially supported by the AFOSR grant FA9550-14-1-0275. The work of C. Tsogka was partially supported by the European Research Council Starting Grant, GA 239959 and the AFOSR grant FA9550-14-1-0275. This work was in part carried out while C. Tsogka was a visiting Professor at the Mathematics Department at Stanford University.

Notes

No potential conflict of interest was reported by the authors.

1 The quote stands for the fact that clutter backscatter does not give a usual noise matrix with identically distributed and uncorrelated entries, such as Gaussian.

2 In the simulations, the basis (4.1(4.1) ) is discretized at the points t of the interval , and the frequencies sample the same bandwidth in steps , that increase with the tree level l. The implementation uses the Wavelab 850 MATLAB package [21] with window option ‘Sine’.

Additional information

Funding

This work was partially supported by a NAKFI Imaging Science award; NSF [grant number DMS-1510429]; the AFOSR [grant number FA9550-14-1-0275]; European Research Council Starting Grant [GA 239959].