To enable accurate magnetic resonance (MR) parameter mapping with accelerated data acquisition, utilizing recent advances in constrained imaging with sparse sampling.
Theory and Methods
A new constrained reconstruction method based on low-rank and sparsity constraints is proposed to accelerate MR parameter mapping. More specifically, the proposed method simultaneously imposes low-rank and joint sparse structures on contrast-weighted image sequences within a unified mathematical formulation. With a pre-estimated subspace, this formulation results in a convex optimization problem, which is solved using an efficient numerical algorithm based on the alternating direction method of multipliers.
To evaluate the performance of the proposed method, two application examples were considered: (i) T2 mapping of the human brain and (ii) T1 mapping of the rat brain. For each application, the proposed method was evaluated at both moderate and high acceleration levels. Additionally, the proposed method was compared with two state-of-the-art methods that only use a single low-rank or joint sparsity constraint. The results demonstrate that the proposed method can achieve accurate parameter estimation with both moderately and highly undersampled data. Although all methods performed fairly well with moderately undersampled data, the proposed method achieved much better performance (e.g., more accurate parameter values) than the other two methods with highly undersampled data.
Simultaneously imposing low-rank and sparsity constraints can effectively improve the accuracy of fast MR parameter mapping with sparse sampling.
To enable dynamic speech imaging with high spatiotemporal resolution and full-vocal-tract spatial coverage, leveraging recent advances in sparse sampling.
An imaging method is developed to enable high-speed dynamic speech imaging exploiting low-rank and sparsity of the dynamic images of articulatory motion during speech. The proposed method includes: (a) a novel data acquisition strategy that collects spiral navigators with high temporal frame rate and (b) an image reconstruction method that derives temporal subspaces from navigators and reconstructs high-resolution images from sparsely sampled data with joint low-rank and sparsity constraints.
The proposed method has been systematically evaluated and validated through several dynamic speech experiments. A nominal imaging speed of 102 frames per second (fps) was achieved for a single-slice imaging protocol with a spatial resolution of 2.2 × 2.2 × 6.5 mm3. An eight-slice imaging protocol covering the entire vocal tract achieved a nominal imaging speed of 12.8 fps with the identical spatial resolution. The effectiveness of the proposed method and its practical utility was also demonstrated in a phonetic investigation.
High spatiotemporal resolution with full-vocal-tract spatial coverage can be achieved for dynamic speech imaging experiments with low-rank and sparsity constraints.
This paper presents a new method to jointly estimate the spherical harmonic coefficients for all the voxels from noisy magnitude diffusion-weighted images acquired in high angular resolution diffusion imaging. The proposed method uses a penalized maximum likelihood estimation formulation that integrates a noncentral χ distribution based noisy data model, a sparsity promoting penalty on the spherical harmonic coefficients and a joint sparse regularization on the diffusion-weighted image series. An efficient algorithm based on majorize-minimize and alternating direction method of multipliers is proposed to solve the resulting optimization problem. The performance of the proposed method has been evaluated using simulated and experimental data, which demonstrate the improvement over conventional methods in terms of estimation accuracy.
In this paper, we introduce a statistical estimation framework for magnetic resonance fingerprinting (MRF), a recently proposed quantitative imaging paradigm. Within this framework, we present a maximum likelihood formulation to simultaneously estimate multiple parameter maps from highly undersampled, noisy k-space data. A novel iterative algorithm, based on variable splitting, the alternating direction method of multipliers, and the variable projection method, is proposed to solve the resulting optimization problem. Representative results demonstrate that compared to the conventional MRF reconstruction, the proposed method yields improved accuracy and/or reduced acquisition time. Moreover, the proposed formulation enables theoretical analysis of MRF. For example, we show that with the gridding reconstruction as an initialization, the first iteration of the proposed method exactly produces the conventional MRF reconstruction.
Magnetic resonance fingerprinting (MRF) is an emerging quantitative magnetic resonance (MR) imaging technique that simultaneously acquires multiple tissue parameters (e.g., spin density, T1, and T2) in an efficient imaging experiment. A statistical estimation framework has recently been proposed for MRF reconstruction. Here we present a new model-based reconstruction method within this framework to enable improved parameter estimation from highly under-sampled, noisy k-space data. It features a novel mathematical formulation that integrates a low-rank image model with the Bloch equation based MR physical model. The proposed formulation results in a nonconvex optimization problem, for which we develop an efficient iterative algorithm based on variable splitting, the alternating direction method of multipliers, and the variable projection method. Representative results from numerical experiments are shown to illustrate the performance of the proposed method.
Athinoula A. Martinos Center for Biomedical Imaging