Geometry of Deep Learning for Magnetic Resonance Fingerprinting

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study a deep learning approach to address these shortcomings. Coupled with a dimensionality reduction first layer, the proposed MRF-Net is able to reconstruct quantitative maps by saving more than 60 times in memory and computations required for a DM baseline. Fine-grid manifold enumeration i.e. the MRF dictionary is only used for training the network and not during image reconstruction. We show that the MRF-Net provides a piece-wise affine approximation to the Bloch response manifold projection and that rather than memorizing the dictionary, the network efficiently clusters this manifold and learns a set of hierarchical matched-filters for affine regression of the NMR characteristics in each segment

Deep learning-based parameter mapping for joint relaxation and diffusion tensor MR Fingerprinting

Magnetic Resonance Fingerprinting (MRF) enables the simultaneous quantification of multiple properties of biological tissues. It relies on a pseudo-random acquisition and the matching of acquired signal evolutions to a precomputed dictionary. However, the dictionary is not scalable to higher-parametric spaces, limiting MRF to the simultaneous mapping of only a small number of parameters (proton density, T1 and T2 in general). Inspired by diffusion-weighted SSFP imaging, we present a proof-of-concept of a novel MRF sequence with embedded diffusion-encoding gradients along all three axes to efficiently encode orientational diffusion and T1 and T2 relaxation. We take advantage of a convolutional neural network (CNN) to reconstruct multiple quantitative maps from this single, highly undersampled acquisition. We bypass expensive dictionary matching by learning the implicit physical relationships between the spatiotemporal MRF data and the T1, T2 and diffusion tensor parameters. The predicted parameter maps and the derived scalar diffusion metrics agree well with state-of-the-art reference protocols. Orientational diffusion information is captured as seen from the estimated primary diffusion directions. In addition to this, the joint acquisition and reconstruction framework proves capable of preserving tissue abnormalities in multiple sclerosis lesions

Deep Unrolling for Magnetic Resonance Fingerprinting

Magnetic Resonance Fingerprinting (MRF) has emerged as a promising quantitative MR imaging approach. Deep learning methods have been proposed for MRF and demonstrated improved performance over classical compressed sensing algorithms. However many of these end-to-end models are physics-free, while consistency of the predictions with respect to the physical forward model is crucial for reliably solving inverse problems. To address this, recently [1] proposed a proximal gradient descent framework that directly incorporates the forward acquisition and Bloch dynamic models within an unrolled learning mechanism. However, [1] only evaluated the unrolled model on synthetic data using Cartesian sampling trajectories. In this paper, as a complementary to [1], we investigate other choices of encoders to build the proximal neural network, and evaluate the deep unrolling algorithm on real accelerated MRF scans with non-Cartesian k-space sampling trajectories.Comment: Tech report. arXiv admin note: substantial text overlap with arXiv:2006.1527

Rapid three-dimensional multiparametric MRI with quantitative transient-state imaging

Novel methods for quantitative, transient-state multiparametric imaging are increasingly being demonstrated for assessment of disease and treatment efficacy. Here, we build on these by assessing the most common Non-Cartesian readout trajectories (2D/3D radials and spirals), demonstrating efficient anti-aliasing with a k-space view-sharing technique, and proposing novel methods for parameter inference with neural networks that incorporate the estimation of proton density. Our results show good agreement with gold standard and phantom references for all readout trajectories at 1.5T and 3T. Parameters inferred with the neural network were within 6.58% difference from the parameters inferred with a high-resolution dictionary. Concordance correlation coefficients were above 0.92 and the normalized root mean squared error ranged between 4.2% - 12.7% with respect to gold-standard phantom references for T1 and T2. In vivo acquisitions demonstrate sub-millimetric isotropic resolution in under five minutes with reconstruction and inference times < 7 minutes. Our 3D quantitative transient-state imaging approach could enable high-resolution multiparametric tissue quantification within clinically acceptable acquisition and reconstruction times.Comment: 43 pages, 12 Figures, 5 Table

Learning Bloch Simulations for MR Fingerprinting by Invertible Neural Networks

Magnetic resonance fingerprinting (MRF) enables fast and multiparametric MR imaging. Despite fast acquisition, the state-of-the-art reconstruction of MRF based on dictionary matching is slow and lacks scalability. To overcome these limitations, neural network (NN) approaches estimating MR parameters from fingerprints have been proposed recently. Here, we revisit NN-based MRF reconstruction to jointly learn the forward process from MR parameters to fingerprints and the backward process from fingerprints to MR parameters by leveraging invertible neural networks (INNs). As a proof-of-concept, we perform various experiments showing the benefit of learning the forward process, i.e., the Bloch simulations, for improved MR parameter estimation. The benefit especially accentuates when MR parameter estimation is difficult due to MR physical restrictions. Therefore, INNs might be a feasible alternative to the current solely backward-based NNs for MRF reconstruction.Comment: Accepted at MICCAI MLMIR 202