Multicompartment magnetic resonance fingerprinting

Abstract

Magnetic resonance fingerprinting (MRF) is a technique for quantitative estimation of spin- relaxation parameters from magnetic-resonance data. Most current MRF approaches assume that only one tissue is present in each voxel, which neglects intravoxel structure, and may lead to artifacts in the recovered parameter maps at boundaries between tissues. In this work, we propose a multicompartment MRF model that accounts for the presence of multiple tissues per voxel. The model is fit to the data by iteratively solving a sparse linear inverse problem at each voxel, in order to express the measured magnetization signal as a linear combination of a few elements in a precomputed fingerprint dictionary. Thresholding-based methods commonly used for sparse recovery and compressed sensing do not perform well in this setting due to the high local coherence of the dictionary. Instead, we solve this challenging sparse-recovery problem by applying reweighted-𝓁1-norm regularization, implemented using an efficient interior-point method. The proposed approach is validated with simulated data at different noise levels and undersampling factors, as well as with a controlled phantom-imaging experiment on a clinical magnetic-resonance system.

Sparse Recovery Beyond Compressed Sensing: Separable Nonlinear Inverse Problems

“…The continuous optimization problem (2.14) can be solved by applying 1 -norm minimization after discretizing the parameter space. This is a very popular approach in practice for a variety of SNL problems [55,77,84,86,94]. If the true parameters lie on the discretization grid, then our exactrecovery results translate immediately.…”

“…• Quantitative magnetic-resonance imaging: The magnetic-resonance relaxation times T 1 and T 2 of biological tissues govern the local fluctuations of the magnetic field measured by MR imaging systems [63]. MR fingerprinting is a technique to estimate these parameters by fitting an SNL model where each component corresponds to a different tissue [54,57,84]. In this case, the parameter θ ∈ R 2 encodes the values of T 1 and T 2 and the function ϕ t (θ) can be computed by solving the Bloch differential equations [7].…”

“…This approach was pioneered in the 1970s by geophysicists working on spike deconvolution in the context of reflection seismology [22,24,50,74,86]. Since then, it has been applied to many SNL problems such as acoustic sensing [4,94], radar [68,85], electroencephalography (EEG) [77,92], positron emission tomography (PET) [45,47,70], direction of arrival [8,55], quantitative magnetic resonance imaging [57,84], and source localization [52,56,66]. Our goal is to provide a theory of sparse recovery via convex optimization explaining the empirical success of this approach.…”

High‐dimensionality undersampled patch‐based reconstruction (HD‐PROST) for accelerated multi‐contrast MRI

“…The highly undersampled pseudo‐random MRF acquisition results in a high level of noise and aliasing in the reconstructed time point images. Several iterative techniques have been recently proposed to improve the reconstruction quality of each time point image . Zhao et al proposed to enforce low‐rank and subspace modeling in the temporal dimension to reconstruct high‐quality time point images.…”

Magnetic resonance fingerprinting review part 2: Technique and directions

“…c for a glioblastoma brain tumor patient. The work by Tang et al also does not require a fixed tissue model, but instead encourages sparsity of the weight vector by using reweighted ℓ 1 regularization. Although these methods are computationally more complex than the dictionary‐based approach, they allow a more flexible tissue model when relaxation values are not known a priori, which may be the case in diseased or abnormal tissues.…”