Figure 1. Simulation of a cluttered medium: A concrete slab with three defects.
Figure 1. Simulation of a cluttered medium: A concrete slab with three defects.
In applications such as radar and ultrasound imaging, non-destructive testing of materials, etc., we send some signals from one array of antennas or transducers and record the scattered echoes. From this data we wish to identify strong scatterers in the medium. The type of scatterers varies from application to application. For example, in non-destructive testing of materials, we seek defects such as voids and cracks. In seismic imaging we may wish to identify Earth structures such as fault lines. In shallow water or land mine detection the scatterers are mines, and so on.
These problems can be solved well when the scatterers lie in a smooth and known background, as in the case of radar imaging of in-flight aircraft, where the atmosphere is fairly homogeneous.
Our interest lies in the more challenging case of a cluttered background that arises for example in foliage penetrating radar, in non-destructive testing of materials, etc.
Illustrating the latter example, consider a slab as shown in Fig. 1, where we have three defects that we wish to find with ultrasound waves sent and received at the array of transducers on top of the structure. If the concrete were a homogeneous material, the recorded data measured across the array would show clearly sharp scattered echoes at the times it takes to travel from the array to the defects and back. See Fig 2.
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| Figure 1 : Homogeneous medium |
Figure 2 : Inhomogeneous, "cluttered" medium |
However, the concrete is inhomogeneous due to the presence of impurities; the waves are scattered by them and the recorded data looks as in Fig. 3. The echoes from the defects are now hidden in the noise due to the clutter and imaging is much more difficult.
Our group, formed by Dr. Liliana Borcea, and graduate students Fernando G. del Cueto and Layla Issa, and external collaborators George Papanicolaou (Stanford) and Chrysoula Togska (U. Chicago) studies imaging and wave propagation in various cluttered media, for a broad spectrum of applications. Using state of the art techniques in stochastic analysis, statistics, signal processing and numerical simulations, we seek to develop robust imaging methodologies in clutter.
As an illustration of our results, we show in Fig. 4 the numerical results of imaging the three defects in the concrete structure and compose it with traditional approaches that fail in the presence of clutter.
Figure 3 : Comparison of the results of traditional imaging versus our method.
Acknowledgment: Pictures are obtained from joint work with G. Papanicolaou and C. Togska.