Detection of Subsurface Bubbles with Discrete Electromagnetic Geotomography |
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Institution: | 1. School of Management, China University of Mining and Technology, Xuzhou, 221116, China;;2. Jiangsu Energy Economics and Management Research Base, Xuzhou, 221116, China;3. School of Public Administration, China University of Mining and Technology, Xuzhou, 221116, China |
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Abstract: | In electromagnetic geotomography, the inversion is very ill-posed due to the limita- tion of an angular range of projections, and consequently the reconstructed image is different than the true image. Nevertheless, the reconstruction can be much im- proved if we are interested only in a piece of information on the interior volume of the examined object, e.g. detection of some anomalies (bubbles). We assume that the image can be represented by binary values, hence: Discrete Electromagnetic Geotomography (DEG). In this paper, we discuss two discrete image reconstruction algorithms. The first one uses the D.C. programming to find the integer solution to the penalized least-squares problem. The penalty term is based on the Gibbs distribution. In the second one, the mean field annealing is applied to maximize the Gibbs-Boltzmann distribution associated with the penalized least-squares function. The numerical results are presented for noise-free and noisy data. |
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