Abstract: Systems and methods are disclosed for optimizing a sub-sampling pattern for efficient capture of a sub-sampled image to be reconstructed to form a high-resolution image, in a data-driven fashion. For example, Magnetic Resonance Imaging (MRI) scans can be accelerated by under-sampling in k-space (i.e., the Fourier domain). Since the reconstruction model's success depends on the sub-sampling pattern, optimization of the sub-sampling pattern can be combined with optimization of the model, for a given sparsity constraint, using an end-to-end learning operation. A machine-learning model may be trained using full-resolution training 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 training data.