Coherent Interferometric Imaging in Clutter

Coherent interferometry is an array imaging method in which we back propagate, or migrate, crosscorrelations of the traces over appropriately chosen space-time windows, rather than the traces themselves. The size of the space-time windows is critical and depends on two parameters. One is the decoherence frequency, which is proportional to the reciprocal of the delay spread in the traces produced by the clutter. The other is the decoherence length, which also depends on the clutter. As is usual, the clutter is modeled by random fluctations in the medium properties. In isotropic clutter the decoherence length is typically much smaller than the array aperture. In layered random media the decoherence length along the layers can be quite large. We show that when the crosscorrelations of the traces are calculated adaptively then coherent interferometry can provide images that are statistically stable relative to small scale clutter in the environment. This means that the images we obtain are not sensitive to the detailed form of the clutter. They only depend on its overall statistical properties. However, clutter does reduce the resolution of the images by ∗Computational and Applied Mathematics, MS 134, Rice University, 6100 Main Street, Houston, TX 77005-1892.([email protected]) †Department of Mathematics, Stanford University, Stanford, CA 94305. ([email protected]) ‡Department of Mathematics, University of Chicago, Chicago, IL 60637. ([email protected])