Maximum likelihood reconstruction for magnetic resonance fingerprinting

Abstract

This paper introduces a statistical estimation framework for magnetic resonance (MR) fingerprinting, a recently proposed quantitative imaging paradigm. Within this framework, we present a maximum likelihood (ML) formalism to estimate multiple parameter maps directly from highly undersampled, noisy k-space data. A novel algorithm, based on variable splitting, the alternating direction method of multipliers, and the variable projection method, is developed to solve the resulting optimization problem. Representative results from both simulations and in vivo experiments demonstrate that the proposed approach yields significantly improved accuracy in parameter estimation, compared to the conventional MR fingerprinting reconstruction. Moreover, Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. HHS Public Access Author Manuscript Author ManuscriptAuthor ManuscriptAuthor Manuscript the proposed framework provides new theoretical insights into the conventional approach. We show analytically that the conventional approach is an approximation to the ML reconstruction; more precisely, it is exactly equivalent to the first iteration of the proposed algorithm for the ML reconstruction, provided that a gridding reconstruction is used as an initialization.

Low rank alternating direction method of multipliers reconstruction for MR fingerprinting

“…ADMM, like other iterative reconstructions proposed for MRF, constrains the reconstruction directly to atoms of the dictionary (12)(13)(14)20). However, these approaches are nonconvex problems, which are prone to convergence issues.…”

“…The recently proposed application of ADMM (23) to the original MRF (13,14) addresses the reconstruction problem by solving Eq. [14] via variable splitting.…”

“…[18] is nonconvex, such that the convergence of the algorithm depends on the initial guess (13). Here, we initialize the algorithm withx 0 ¼ 0; ðDD H Þ 0 ¼ 1 andỹ 0 ¼ 0.…”

“…Recent developments suggest that significant improvements in image quality can be gained by feeding the data model to the image reconstruction (12)(13)(14). Due to the nonlinear nature of the Bloch equation, the MRF reconstruction problem is generally nonconvex.…”

“…Therefore, global convergence of MRF reconstruction algorithmsincluding the proposed one-is usually not guaranteed and a good initial guess is essential. The present article addresses this issue by a low rank (LR) approximation (15)(16)(17)(18)(19)(20)(21)(22) of the voxels' signal evolution, to which the alternating direction method of multipliers (ADMM) (13,14,23) is applied. The proposed algorithm splits the MRF reconstruction problem into two sub-problems that are solved alternately: A linear inverse problem with data consistency at its core and a dictionary matching step.…”