PIERRE LOBEL'S THESIS

Inverse scattering problems : image reconstruction and enhancement with edge-preserving regularization -- Application to microwave imaging

Summary

This thesis deals with image reconstruction in microwave domain, and more generally with inverse scattering problems. Due to its nonlinearity and its ill-posedness, the inverse scattering problem is particulary complex. It leads to the minimization of a nonlinear system and several methods have been proposed, in the past fifteenth years, to solve it, with a quantitative approach. We present a method based a on conjugate gradient (CG) algorithm for solving it. This method uses a unique nonlinear cost-functional to minimize, which comes from the application of the moment method on the integral representation of the electric field. Good results have been obtained from synthetic and experimental data. A study on the influence of the initial guess calculed with a backpropagation scheme hase also been made. In order to reconstruct images from noisy corrupted data, or from high values contrast data, the introduction of some regularization process is needed. We develop a nonlinear regularization method based on the use of Markov Random Fields. It leads to the smoothing of the homogeneous areas of the images, while edges are preserved. We apply this method on the CG algorithm and also on a Newton-Kantorovitch type one. A significant enhancement has been obtained from noisy corrupted synthetic and experimental data.

Keywords

Inverse scattering problem, Ill-posedness, Nonlinearity, Regularization, Edge preserving, Markov Random Fields, Potential function, Conjugate Gradient, Alternate minimization, Microwave tomography.

Commitee

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