Ensemble Average Propagator Reconstruction Via Compressed Sensing: Discrete or Continuous Bases ?

Sylvain Louis Merlet¹, Michael Paquette², Rachid Deriche³, Maxime Descoteaux²

Sparsity is one of the key ingredient in Compressed Sensing recovery. In Diffusion MRI, few studies have been proposed to characterize the sparsity of the Ensemble Average Propagator which captures the water diffusion phenomenon. We propose a fair comparison of two classes of representations : The discrete representations, via the Haar, Daubechie-Cohen-Fauveau (DCF) 5-3, DCF 9-7 wavelets bases, and the continuous representations, via Spherical Polar Fourier (SPF) and 3D Simple Harmonic Oscillation Reconstruction and Estimation (SHORE) bases. We study the advantages and disadvantages of these discrete and continuous representations EAP for the first time.