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Intégration de connaissances a priori dans la reconstruction des signaux parcimonieux : Cas particulier de la spectroscopie RMN multidimensionnelle

Dany Merhej 1
1 Images et Modèles
CREATIS - Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé
Abstract : The work of this thesis concerns the proposal of algorithms for the integration of prior knowledge in the reconstruction of sparse signals. The purpose is mainly to improve the reconstruction of these signals from a set of measurements well below what is requested by the famous theorem of Shannon-Nyquist. In the first part we propose, in the context of the new theory of "compressed sensing" (CS), the algorithm NNOMP (Neural Network Orthogonal Matching Pursuit), which is a modified version of the algorithm OMP in which we replaced the correlation step by a properly trained neural network. The goal is to better reconstruct sparse signals with additional structures, i.e. belonging to a particular model of sparse signals. For the experimental validation of NNOMP three simulated models of sparse signals with additional structures were considered and a practical application in an arrangement similar to the “single pixel imaging”. In the second part, we propose a new method for under sampling in multidimensional NMR spectroscopy (including NMR spectroscopic imaging), when the corresponding spectra of lower dimensional acquisitions, e.g. one-dimensional, are intrinsically sparse. In this method, we model the whole process of data acquisition and reconstruction of multidimensional spectra, by a system of linear equations. We then use a priori knowledge about the non-zero locations in multidimensional spectra, to remove the under-determinacy induced by data under sampling. This a priori knowledge is obtained from the lower dimensional acquisition spectra, e.g. one-dimensional. The possibility of under sampling increases proportionally with the sparsity of these one dimensional spectra. The proposed method is evaluated on synthetic, experimental in vitro and in vivo data.
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Dany Merhej. Intégration de connaissances a priori dans la reconstruction des signaux parcimonieux : Cas particulier de la spectroscopie RMN multidimensionnelle. Autre. INSA de Lyon, 2012. Français. ⟨NNT : 2012ISAL0014⟩. ⟨tel-00782465⟩

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