Regularized Spherical Polar Fourier Diffusion MRI with Optimal Dictionary

Abstract. Compressed Sensing (CS) takes advantage of signal sparsity or com-pressibility and allows superb signal reconstruction from relatively few measure-ments. Based on CS theory, a suitable dictionary for sparse representation of the signal is required. In diffusion MRI (dMRI), CS methods were proposed to recon-struct diffusion-weighted signal and the Ensemble Average Propagator (EAP), and there are two kinds of Dictionary Learning (DL) methods: 1) Discrete Repre-sentation DL (DR-DL), and 2) Continuous Representation DL (CR-DL). DR-DL is susceptible to numerical inaccuracy owing to interpolation and regridding er-rors in a discretized q-space. In this paper, we propose a novel CR-DL approach, called Dictionary Learning- Spherical Polar Fourier Imaging (DL-SPFI) for ef-fective compressed-sensing reconstruction of the q-space diffusion-weighted sig-nal and the EAP. In DL-SPFI, an dictionary that sparsifies the signal is learned from the space of continuous Gaussian diffusion signals. The learned dictionary is then adaptively applied to different voxels using a weighted LASSO framework for robust signal reconstruction. The adaptive dictionary is proved to be opti