Level set methods in 2D cross-borehole tomography

joint work with
E Miller and C Rappaport, CenSSIS, Northeastern University, Boston, USA

In the project, we have developed a level-set based shape reconstruction algorithm in 2D for imaging buried objects from limited-view multi-frequency cross-borehole electromagnetic data.

A.) Here is an example with full view to the scenery. Electromagnetic sources and receivers completely surround the domain of interest. The object to be reconstructed is shown in the figure below.

The level set based shape evolution is shown next. Notice that the 'hole' in the house is recovered without any problems by the method.

B.) Here is a geophysical example with limited view. Given cross-borehole EM data, the three buried objects need to be reconstructed. Here, due to the limited view to the domain of interest, the main difficulty is to separate the two upper objects from each other.

The shape evolution for this example can be seen below. The level set based shape reconstruction algorithm has no difficulties in solving the task.

Here are some more results of our numerical experiments:

Publications:

1. 'A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets', to appear in Inverse Problems, special issue on 'Electromagnetic Imaging and Inversion of the Earth's Subsurface', October 2000 issue (Invited Paper).

PDF file (1.6 MByte)
PS file not including figures 15 and 16 (3.9 MByte)
PS file figure 15 (2.0 MByte)
PS file figure 16 (3.8 MByte)

2. 'Shape reconstruction in 2D from limited-view multifrequency electromagnetic data' (accepted for publication)

PS file (4.4 MByte)

PDF file (370 KByte)

The levelART algorithm

An example with full view:

original (ps-file) , (jpeg figure)
shape evolution (ps-file)
final reconstruction (ps-file) , (jpeg figure)

A cross-borehole example with limited view:

original (ps-file) , (jpeg figure)
shape evolution 1 (no noise, no curve shortening) (ps-file)
final reconstruction 1 (ps-file) , (jpeg figure)
shape evolution 2 (no noise, with curve shortening) (ps-file)
final reconstruction 2 (ps-file) , (jpeg figure)
shape evolution 3 (noisy data with SNR 10 dB, no curve shortening) (ps-file)
final reconstruction 3 (ps-file) , (jpeg figure)
shape evolution 4 (noisy data with SNR 10 dB, with curve shortening) (ps-file)
final reconstruction 4 (ps-file) , (jpeg figure)
shape evolution 5 (noisy data with SNR 5 dB, with curve shortening) (ps-file)
final reconstruction 5 (ps-file) , (jpeg figure)

This page was created on 28 April 2000 and last changed on 28 April 2000..