Adaptive time-frequency detection and filtering for imaging in strongly heterogeneous background media
Seminar Room 1, Newton Institute
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 experiments. While the detection and filtering algorithm that we present works well in general clutter it has been analyzed theoretically only for the case of randomly layered media.