PIERRE LOBEL
Sr. Embedded Software Engineer
Thesis
Title
Inverse scattering problems : image reconstruction and enhancement with
edge-preserving regularization -- Application to microwave imaging
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.
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.
Markov Random Fields, Potential function, Conjugate Gradient, Alternate minimization,
Microwave tomography.
Jury
Directeur de Recherche CNRS
Président
M. Daniel MAYSTRE
M. Alfred K. LOUIS
Rapporteur
Professeur, Université de Sarrebrück
M. Ralph E. KLEINMAN
Professeur, Université du Delaware
Rapporteur
M. Alois J. SIEBER
Directeur ATU/EMSL, JRC, Ispra
Rapporteur
M. Michel BARLAUD
Professeur, UNSA
Directeur de thèse
M. Christian PICHOT
Directeur de thèse
Directeur de Recherche CNRS
Mme Laure BLANC-FÉRAUD
Examinatrice
Chargé de Recherche CNRS
M. Albert PAPIERNIK
Professeur, UNSA
Examinatrice
