Abstract : Compressed Sensing (CS) or Compressive Sampling is a recent technique to accurately reconstruct sparse signals from under sampled measurements acquired below the Shannon-Nyquist rate. In this article, we present a CS based method for accelerating the reconstruction of the Ensemble Average Propagator (EAP), also known as the Propagator in Diffusion MRI (dMRI), by significantly reducing the number of measurements. Contrarily to the time consuming acquisition technique known as the Diffusion Spectrum Imaging (DSI), our method is developed and implemented to efficiently reconstruct the EAP from reduced and non uniformly under sampled Diffusion Weighted (DW) MRI images combined to an efficient and accurate l1 norm based reconstruction algorithm. We illustrate in detail the artifacts occurring in a classical EAP reconstruction à la DSI, and qualitatively and quantitatively demonstrate good and better results in recovering the EAP and some of its important features such as the Orientation Distribution Function ( ODF) from non-regularly undersampled and l1 norm based reconstructed data. This opens an original and very interesting road to shorten the dMRI acquisition time and opens new opportunities to render High Angular Resolution Diffusion Imaging (HARDI) feasible in a clinical setting.
