MAPL1: q‐space reconstruction using ‐regularized mean apparent propagator

Abstract

Purpose To improve the quality of mean apparent propagator (MAP) reconstruction from a limited number of q‐space samples. Methods We implement an ℓ1‐regularised MAP (MAPL1) to consider higher order basis functions and to improve the fit without increasing the number of q‐space samples. We compare MAPL1 with the least‐squares optimization subject to non‐negativity (MAP), and the Laplacian‐regularized MAP (MAPL). We use simulations of crossing fibers and compute the normalized mean squared error (NMSE) and the Pearson’s correlation coefficient to evaluate the reconstruction quality in q‐space. We also compare coefficient‐based diffusion indices in the simulations and in in vivo data. Results Results indicate that MAPL1 improves NMSE in 1 to 3% when compared to MAP or MAPL in a high undersampling regime. Additionally, MAPL1 produces more reproducible and accurate results for all sampling rates when there are enough basis functions to meet the sparsity criterion for the regularizer. These improved reconstructions also produce better coefficient‐based diffusion indices for in vivo data. Conclusions Adding an ℓ1 regularizer to MAP allows the use of more basis functions and a better fit without increasing the number of q‐space samples. The impact of our research is that a complete diffusion spectrum can be reconstructed from an acquisition time very similar to a diffusion tensor imaging protocol.

Automatic determination of the regularization weighting for wavelet‐based compressed sensing MRI reconstructions

“…For example, the L‐curve 9 method searches for a that equally favors the data consistency and the regularization terms; the generalized cross validation 10 method with its variants 12 searches for a that minimizes a functional between the acquired data and the reconstruction method; and finally, Stein’s unbiased risk estimate 11 with its variants 12‐14 assumes a certain noise distribution and it searches for a to minimize the MSE. Moreover, because most of these methods for automatic selection of rely in optimality through MSE, an alternative for MRI research using CS‐based approaches has been to determine by comparing the reconstruction to the fully sampled data 15‐20 . Although it may be justifiable to determine as a linear function of the undersampling factor like in Schloegl et al, 21 where slope and constant parameters are learned from fully sampled acquisitions, this procedure would require to be repeated for any change to acquisition parameters.…”

“…Moreover, because most of these methods for automatic selection of rely in optimality through MSE, an alternative for MRI research using CS-based approaches has been to determine by comparing the reconstruction to the fully sampled data. [15][16][17][18][19][20] Although it may be justifiable to determine as a linear function of the undersampling factor like in Schloegl et al, 21 where slope and constant parameters are learned from fully sampled acquisitions, this procedure would require to be repeated for any change to acquisition parameters. The objective of using CS approaches is to reduce scan time, and fully sampled acquisitions runs counter to this.…”