NEMAIRE , Masimba

Inverse potential problems permeate many branches of science and engineering especially in non-destructive imaging hence their study is important to the advancement of science and engineering. The inverse problems we study in the thesis are governed by the quasi-static approximation of Maxwell's equations. In the first part of this thesis we...

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In the present article, we study the discrete spectrum of certain bounded Toeplitz operators with harmonic symbol on a Bergman space. Using the methods of classical perturbaton theory and recent results by Borichev-Golinskii-Kupin and Favorov-Golinskii, we obtain a quantitative result on the distribution of the discrete spectrum of the operator...

We study the inverse problems of source recovery and cortical mapping for sEEG, EEG and MEG under the quasi-static approximation of Maxwell's equations. These problems are known to be ill-posed due to the existence of silent source, i.e, those non-zero sources that generate null field. In addition the collected data are corrupted with noise...

We study the inverse source (primary current) localisation problem using the electrical potential measured point-wise inside the head with stereo-ElectroEncephaloGraphy (sEEG), the electrical potential measured point-wise on the scalp with ElectroEncephaloGraphy (EEG) or the magnetic flux density measured point-wise outside the head with...