An empirical study of the maximum degree of undersampling in compressed sensing for T₂^*-weighted MRI

Magnetic Resonance Imaging (MRI) is one of the most dynamic and safe imaging modalities used in clinical routine today. Yet, one major limitation to this technique resides in its long acquisition times. Over the last decade, Compressed Sensing (CS) has been increasingly used to address this issue and offers to shorten MR scans by reconstructing images from undersampled Fourier data. Nevertheless, a quantitative guide on the degree of acceleration applicable to a given acquisition scenario is still lacking today, leading in practice to a trial-and-error approach in the selection of the appropriate undersampling factor. In this study, we shortly point out the existing theoretical sampling results in CS and their limitations which motivate the focus of this work: an empirical and quantitative analysis of the maximum degree of undersampling allowed by CS in the specific context of T₂^*-weighted MRI. We make use of a generic method based on retrospective undersampling to quantitatively deduce the maximum acceleration factor R_max which preserves a desired image quality as a function of the image resolution and the available signal-to-noise ratio (SNR). Our results quantify how larger acceleration factors can be applied to higher resolution images as long as a minimum SNR is guaranteed. In practice however, the maximum acceleration factor for a given resolution appears to be constrained by the available SNR inherent to the considered acquisition. Our analysis enables to take this a priori knowledge into account, allowing to derive a sequence-specific maximum acceleration factor adapted to the intrinsic SNR of any MR pipeline. These results obtained on an analytical T₂^*-weighted phantom image were corroborated by prospective experiments performed on MR data collected with radial trajectories on a 7 T scanner with the same contrast. The proposed framework allows to study other sequence weightings and therefore better optimize sequences when accelerated using CS.