Le cancer du sein est aujourd’hui le cancer le plus fréquent chez la femme ainsi que la première cause de décès féminin par cancer. Actuellement, l’IRM mammaire n’est réalisée qu’en seconde intention lorsque les autres modalités d’imagerie ne suffisent pas à poser un diagnostic. Dans le cas des populations à risque, l’IRM mammaire est recommandée comme examen de dépistage annuel en raison de sa très haute sensibilité de détection. Par IRM, la détection d’un cancer du sein se fait à la suite de l’injection d’un produit de contraste qui permet de visualiser les lésions mammaires en hypersignal. La majeure partie du diagnostic repose sur l’analyse morphologique de ces lésions ; une acquisition hautement résolue spatialement est donc nécessaire. Malgré l’utilisation des techniques d’accélération courantes, le volume de données à acquérir reste important et la résolution temporelle de l’examen d’IRM mammaire est aujourd’hui aux alentours d’une minute. Cette faible résolution temporelle limite donc intrinsèquement la spécificité de l’examen d’IRM mammaire. Un examen avec une haute résolution temporelle permettrait l’utilisation de modèles pharmacocinétiques donnant accès à des paramètres physiologiques spécifiques des lésions. L’approche proposée dans ce travail de thèse est le développement d’une séquence IRM permettant à la fois la reconstruction classique d’images, telle que celle utilisée en routine clinique pour le diagnostic, ainsi qu’une reconstruction accélérée d’images avec une plus haute résolution temporelle permettant ainsi l’application de modèles pharmacocinétiques. Le développement de cette séquence a été réalisé en modifiant l’ordre d’acquisition du domaine de Fourier de la séquence utilisée en clinique, afin qu’il soit aléatoire et permette la reconstruction a posteriori de domaines sous-échantillonnés acquis plus rapidement. Des acquisitions sur des objets tests, sur des volontaires et sur des patientes ont montré que l’acquisition aléatoire ne modifiait pas les images obtenues par reconstruction classique permettant ainsi le diagnostic conventionnel. Une attention particulière a été portée pour permettre la suppression de graisse nécessaire à l’acquisition des images d’IRM mammaire. Les reconstructions des domaines sous-échantillonnés sont réalisées via des reconstructions Compressed Sensing permettant la suppression des artéfacts de sous-échantillonnage. Ces reconstructions Compressed Sensing ont été développées et testées sur des fantômes numériques reproduisant des IRMs mammaires. Le potentiel de cette nouvelle acquisition a enfin été testé sur une lésion artificielle mammaire, développée à cet effet, et reproduisant des prises de contraste mammaires / Breast cancer is nowadays the first cause of female cancer and the first cause of female death by cancer. Breast MRI is only performed in second intention when other imaging modalities cannot lead to a confident diagnosis. In high risk women population, breast MRI is recommended as an annual screening tool because of its higher sensitivity to detect breast cancer. Breast MRI needs contrast agent injection to visualize enhancing lesions and the diagnosis is mostly based on morphological analysis of these lesions. Therefore, an acquisition with high spatial resolution is needed. Despite the use of conventional MRI acceleration techniques, the volume of data to be acquired remains quite large and the temporal resolution of the exam is around one minute. This low temporal resolution may be the cause of the low specificity of breast MRI exam. Breast MRI with higher temporal resolution will allow the use of pharmacokinetic models to access physiological parameters and lesion specifications. The main aim of this work is to develop a MRI sequence allowing a flexible use of the acquired data at the reconstruction stage. On the one hand, the images can be reconstructed with a conventional reconstruction like the protocol used in clinical routine. On the other hand, the new MRI sequence will also allow the reconstruction of images with a higher temporal resolution allowing the use of pharmacokinetic models. The development of this sequence was done by modifying the acquisition order in the Fourier domain. A random acquisition of the Fourier domain will allow the reconstruction of sub-sampled domains acquired faster. We paid attention to fat suppression efficiency with this new Fourier domain acquisition order. Tests were performed on phantom, female volunteers and patients. These tests showed that the random acquisition did not impact the quality of images (MRI signal and lesion morphology) obtained by conventional reconstruction thus allowing the conventional diagnosis. The reconstructions of the sub-sampled Fourier domains were made using Compressed Sensing reconstructions to remove sub-sampling artifacts. These reconstructions were developed and tested on digital phantoms reproducing breast MRI. The potential of this new MRI acquisition was tested on an artificial enhancing breast lesion developed especially for this purpose

Compressed Sensing (CS) is a new paradigm in signal processing which exploits the sparse or compressible nature of the signal to significantly reduce the number of measurements, without compromising on the signal reconstruction quality. Recently, many algorithms have been reported in the literature for efficient sparse signal reconstruction. Nevertheless, it is well known that the performance of any sparse reconstruction algorithm depends on many parameters like number of measurements, dimension of the sparse signal, the level of sparsity, the measurement noise power, and the underlying statistical distribution of the non-zero elements of the signal. It has been observed that a satisfactory performance of the sparse reconstruction algorithm mandates certain requirement on these parameters, which is different for different algorithms. Many applications are unlikely to fulfil this requirement. For example, imaging speed is crucial in many Magnetic Resonance Imaging (MRI) applications. This restricts the number of measurements, which in turn affects the medical diagnosis using MRI. Hence, any strategy to improve the signal reconstruction in such adverse scenario is of substantial interest in CS. Interestingly, it can be observed that the performance degradation of the sparse recovery algorithms in the aforementioned cases does not always imply a complete failure. That is, even in such adverse situations, a sparse reconstruction algorithm may provide partially correct information about the signal. In this thesis, we study this scenario and propose a novel fusion framework and an iterative framework which exploit the partial information available in the sparse signal estimate(s) to improve sparse signal reconstruction. The proposed fusion framework employs multiple sparse reconstruction algorithms, independently, for signal reconstruction. We first propose a fusion algorithm viz. FACS which fuses the estimates of multiple participating algorithms in order to improve the sparse signal reconstruction. To alleviate the inherent drawbacks of FACS and further improve the sparse signal reconstruction, we propose another fusion algorithm called CoMACS and variants of CoMACS. For low latency applications, we propose a latency friendly fusion algorithm called pFACS. We also extend the fusion framework to the MMV problem and propose the extension of FACS called MMV-FACS. We theoretically analyse the proposed fusion algorithms and derive guarantees for performance improvement. We also show that the proposed fusion algorithms are robust against both signal and measurement perturbations. Further, we demonstrate the efficacy of the proposed algorithms via numerical experiments: (i) using sparse signals with different statistical distributions in noise-free and noisy scenarios, and (ii) using real-world ECG signals. The extensive numerical experiments show that, for a judicious choice of the participating algorithms, the proposed fusion algorithms result in a sparse signal estimate which is often better than the sparse signal estimate of the best participating algorithm. The proposed fusion framework requires toemploy multiple sparse reconstruction algorithms for sparse signal reconstruction. We also propose an iterative framework and algorithm called {IFSRA to improve the performance of a given arbitrary sparse reconstruction algorithm. We theoretically analyse IFSRA and derive convergence guarantees under signal and measurement perturbations. Numerical experiments on synthetic and real-world data confirm the efficacy of IFSRA. The proposed fusion algorithms and IFSRA are general in nature and does not require any modification in the participating algorithm(s).