Low-rank and sparsity-based models in Magnetic Resonance Imaging (B03)

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In this project, we aim at a deeper mathematical understanding of the different recent approaches to parallel Magnetic Resonance Imaging (MRI) which are based on regularization and subspace methods. Using the underlying Fourier analysis background of the current methods, we will develop new efficient algorithms for parallel MRI. We will use qualitative prior knowledge about the image and the coil sensitivities in a principled way in the regularization methods and employ low-rank approximation of structured matrices and sparsity in adaptive bases in Fourier domain.