Physically plausible K-space trajectories for Compressed Sensing in MRI: From simulations to real acquisitions
Résumé
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to image the anatomy and function of the body in both health and disease. MRI is probably one of the most successful application fields of compressed sensing (CS). Despite recent advances, there is still a large discrepancy between theories and actual applications. Overall, many important questions related to sampling theory remain open. In this work, we address one of them: given a set of hardware constraints (e.g. sampling Fourier coefficients along smooth curves), how to optimally design a sampling pattern? We first derive three key aspects that should be carefully designed by inspecting the literature, namely admissibility, limit of the empirical measure and coverage speed. To fulfill them jointly, we then propose an original approach which consists of projecting a probability distribution onto a set of admissible measures. The proposed algorithm allows to handle arbitrary hardware constraints (gradient magnitude, slew rate) and then automatically generates efficient sampling patterns. The MR images reconstructed using the proposed approach have a significantly higher SNR (2-3 dB) than those reconstructed using more standard sampling patterns (e.g. radial, spiral), both for medium and very high resolution imaging. Likewise, reconstructions from highly undersampled data acquired in experiments performed on a 7T SIEMENS MR scanner show the superiority of our sampling schemes over traditional MR samplings and proved that very large acceleration factor (up to 40-fold) are practically achievable with CS-MRI.
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