Compressed sensing of diffusion MRI data using spatial regularization and positivity constraints

In recent years, there has been an ever increasing number of works reporting the successful application of the theory of compressed sensing (CS) to the problem of time-efficient reconstruction of MRI scans. The CS theory seems to be particularly advantageous in application to diffusion MRI (dMRI), where, for the same region of interest, a number of MRI scans need to be acquired in order to assess the strength of water diffusion along different spatial directions. In this paper, we propose a CS-based reconstruction method which allows a substantial reduction in the number of diffusion encoding gradients required for reliable estimation of high angular resolution diffusion imaging signals. Specifically, the method performs a CS-based reconstruction in the diffusion domain subject to two additional constraints, namely: 1) the diffusion signals have to be spatially regular, and 2) the diffusion signals have to be non-negative valued. Additionally, we detail an efficient numerical solution based on variable splitting and proximity operations, which can be used to perform the proposed reconstruction. The paper is concluded with experimental results which support the practical value of our methodology.