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MAPL1: q ‐space reconstruction using ℓ 1 ‐regularized mean apparent propagator
Author(s) -
VarelaMattatall Gabriel,
CastilloPassi Carlos,
Koch Alexandra,
Mura Joaquin,
Stirnberg Rüdiger,
Uribe Sergio,
Tejos Cristian,
Stöcker Tony,
Irarrazaval Pablo
Publication year - 2020
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.28268
Subject(s) - undersampling , mathematics , basis (linear algebra) , basis function , diffusion mri , algorithm , mathematical analysis , artificial intelligence , computer science , geometry , medicine , magnetic resonance imaging , radiology
Purpose To improve the quality of mean apparent propagator (MAP) reconstruction from a limited number of q ‐space samples. Methods We implement an ℓ 1 ‐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 ℓ 1 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.