The long scan times of Magnetic Resonance Imaging (MRI) create a bottleneck in patient care and acquisitions can be accelerated by under-sampling in k-space (i.e., the Fourier domain). In this thesis, we focus on the optimization of the sub-sampling pattern with a data-driven framework. Since the reconstruction quality of the models are shown to be strongly dependent on the sub-sampling pattern, we combine the two problems. For a provided sparsity constraint, our method optimizes the sub-sampling pattern and reconstruction model, using an end-to-end unsupervised learning strategy. Our algorithm is trained on full-resolution data that are under-sampled retrospectively, yielding a sub-sampling pattern and reconstruction model that are customized to the type of images represented in the data set. The proposed method, which we call LOUPE (Learning-based Optimization of the Under-sampling PattErn), was implemented by modifying a U-Net, a widely-used convolutional neural network architecture, that we append with the forward model that encodes the under-sampling process. Our experiments with T1- weighted structural brain MRI scans, PD and PDFS weighted knee MRI scans show that the optimized sub-sampling pattern can yield significantly more accurate reconstructions compared to standard random uniform, variable density or cartesian under-sampling schemes. The code is made available at: https: //github.com/cagladbahadir/LOUPE .