Optimal real-time q-ball imaging with incremental recursive orientation sets

INTRODUCTION: High angular resolution diffusion imaging (HARDI) requires more diffusion-weighted (DW) measurements than traditional diffusion tensor imaging acquisitions, but it can resolve some fibre crossings. This comes at the price of a longer acquisition time, which can be problematic for clinical studies involving children and people inflicted with certain diseases. Excessive motion of the patient during the acquisition process can force an acquisition to be aborted or make the diffusion weighted images useless. Thus, one would like to make only as many acquisitions as is necessary. According to the literature, this number is likely to be somewhere between 50 and 200 DW measurements but this is still an open question. Recently, Poupon et al. [1], addressed this issue and proposed an algorithm for real-time estimation of the diffusion tensor and the orientation distribution function (ODF) from q-ball imaging (QBI) using the Kalman filtering framework. However, this solution is in fact optimal only for the last iteration of the q-ball ODF estimation, and sub-optimal at earlier iterations. This is problematic for the intended real-time QBI system. As we would like to stop the acquisition at any time or as soon as the ODF estimation has converged, a good estimation of the ODF is highly desirable at the beginning of the acquisition and thus, the development of an optimal and incremental solution is important. In this work, we adapt the Kalman filtering solution to correctly incorporate the regularization into the filter parameters without changing the ODF reconstruction model [2]. The basic idea is to go back to the derivation of the Kalman filtering equations and include this regularization term. Moreover, in order for this framework to be fully incremental and take its full power in real-time, we also tackle the problem of the optimal choice of the DW gradient orientation set. Typically, each measurement is acquired along a given orientation extracted from an optimised set of orientations estimated and ordered off-line [3]-[6], before the acquisition is started. Hence, we propose a fast algorithm to recursively compute gradient orientation sets whose partial subsets are almost uniform.