Comparison of q-space reconstruction methods for undersampled diffusion spectrum imaging data

Abstract

Purpose: To compare different q-space reconstruction methods for undersampled diffusion spectrum imaging data. Materials and Methods: We compared the quality of three methods: Mean Apparent Propagator (MAP); Compressed Sensing using Identity (CSI) and Compressed Sensing using Dictionary (CSD) with simulated data and in vivo acquisitions. We used retrospective undersampling so that the fully sampled reconstruction could be used as ground truth. We used the normalized mean squared error (NMSE) and the Pearson’s correlation coefficient as reconstruction quality indices. Additionally, we evaluated two propagator-based diffusion indices: mean squared displacement and return to zero probability. We also did a visual analysis around the centrum semiovale. Results: All methods had reconstruction errors below 5% with low undersampling factors and with a wide range of noise levels. However, the CSD method had at least 1–2% lower NMSE than the other reconstruction methods at higher noise levels. MAP was the second-best method when using a sufficiently high number of q-space samples. MAP reconstruction showed better propagator-based diffusion indices for in vivo acquisitions. With undersampling factors greater than 4, MAP and CSI have noticeably more reconstruction error than CSD. Conclusion: Undersampled data were best reconstructed by means of CSD in simulations and in vivo. MAP was more accurate in the extraction of propagator-based indices, particularly for in vivo data.