Deep learning for MR image reconstruction
My PhD will be focused on designing the best neural network architecture for MR image reconstruction from undersampled data. MR image reconstruction basically consists in doing an inverse Fourier transform from undersampled (in the sense of Nyquist-Shannon) fourier data. The theory of compressed sensing tells us it's possible if the original data has some sparsity in a particular domain, here the wavelet decomposition.
Convex Optimisation for non smooth inverse problems
In order to understand the current state of the art of MR image reconstruction, I need to understand how the current compressed sensing strategies work. It involves solving an inverse problem via convex non smooth optimisation.