Adaptive Time-Frequency Detection and Filtering for Imaging in Strongly Heterogeneous Background Media

Abstract eng:
We consider the problem of detecting and imaging the location of compactly supported reflectors embedded in strongly heterogeneous background media. Imaging in such regimes is quite challenging as the incoherent wave field that is produced from reflections by the background medium overwhelms the scattered field from the object that wish to image. To detect the presence of a reflector in such regimes we introduce an adaptive time-frequency representation of the array response matrix followed by a Singular Value Decomposition (SVD). The detection is adaptive because the time windows that contain the primary echoes from the reflector are not determined in advance. Their location and width is determined by searching through the time-frequency binary tree of the LCT. After detecting the presence of the reflector we filter the array response matrix to retain information only in the time windows that have been selected. We also project the filtered array response matrix to the subspace associated with the top singular value and then image using travel time migration. We show with extensive numerical simulations that this approach to detection and imaging works well in heavy clutter that is calibrated using random matrix theory so as to simulate regimes close to the experiments in [2]. While the detection and filtering algorithm presented here (cf. also [3]) works well in general clutter it has been analyzed theoretically only for the case of randomly layered media [1]. 056.txt.txt 057.txt.txt 059.txt.txt 060.txt.txt 062.txt.txt 064.txt.txt 066.txt.txt 067.txt.txt 069.txt.txt 070.txt.txt 071.txt.txt 073.txt.txt 074.txt.txt 075.txt.txt 076.txt.txt 079.txt.txt 080.txt.txt 082.txt.txt 083.txt.txt 084.txt.txt 085.txt.txt 086.txt.txt 087.txt.txt 089.txt.txt 091.txt.txt 092.txt.txt 094.txt.txt 095.txt.txt 096.txt.txt 097.txt.txt 098.txt.txt 100.txt.txt 101.txt.txt 103.txt.txt 104.txt.txt 105.txt.txt 106.txt.txt 107.txt.txt 108.txt.txt 109.txt.txt 110.txt.txt 111.txt.txt 115.txt.txt 117.txt.txt 118.txt.txt 119.txt.txt 120.txt.txt 121.txt.txt 122.txt.txt 123.txt.txt 124.txt.txt 125.txt.txt 127.txt.txt 128.txt.txt 131.txt.txt 132.txt.txt 133.txt.txt 134.txt.txt 135.txt.txt 137.txt.txt 139.txt.txt 141.txt.txt 142.txt.txt 143.txt.txt 145.txt.txt 147.txt.txt 148.txt.txt 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References [1] R. Alonso, L. Borcea, G. Papanicolaou, and C. Tsogka, Detection and imaging in strongly backscattering randomly layered media. Preprint 2010. [2] A. Aubry and A. Derode, Detection and imaging in a random medium: A matrix method to overcome multiple scattering and aberration, J.APPL.PHYS., 106 (2009), p. 044903. [3] L. Borcea, G. Papanicolaou, C. Tsogka, Adaptive time-frequency detection and filtering for imaging in heavy clutter. Preprint 2010.

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