Magnetic resonance (MR) fingerprinting is an emerging quantitative MR imaging technique that simultaneously acquires multiple tissue parameters in an efficient experiment. In this work, we present an estimation-theoretic framework to evaluate and design MR fingerprinting experiments. More specifically, we derive the Cramer-Rao bound (CRB), a lower bound on the covariance of any unbiased estimator, to characterize parameter estimation for MR fingerprinting. We then formulate an optimal experiment design problem based on the CRB to choose a set of acquisition parameters (e.g., flip angles and/or repetition times) that maximizes the signal-to-noise ratio efficiency of the resulting experiment. The utility of the proposed approach is validated by numerical studies. Representative results demonstrate that the optimized experiments allow for substantial reduction in the length of an MR fingerprinting acquisition, and substantial improvement in parameter estimation performance.
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.
MR parameter mapping (e.g., T1 mapping, T2 mapping, or T*2 mapping) is a valuable tool for tissue characterization. However, its practical utility has been limited due to long data acquisition time. This paper addresses this problem with a new model-based parameter mapping method, which utilizes an explicit signal model and imposes a sparsity constraint on the parameter values. The proposed method enables direct estimation of the parameters of interest from highly undersampled, noisy k-space data. An algorithm is presented to solve the underlying parameter estimation problem. Its performance is analyzed using estimation-theoretic bounds. Some representative results from T2 brain mapping are also presented to illustrate the performance of the proposed method for accelerating parameter mapping.
Magnetic resonance imaging (MRI) has long been recognized as a powerful tool for cardiovascular imaging because of its unique potential to measure blood flow, cardiac wall motion and tissue properties jointly. However, many clinical applications of cardiac MRI have been limited by low imaging speed. Three-dimensional cardiovascular MRI in real-time, or 4D cardiovascular MRI without cardiac and respiratory gating or triggering, remains an important technological goal of the MR cardiovascular research community. In this paper, we present a novel technique to achieve 4D cardiovascular MR imaging in unprecedented spatiotemporal resolution. This breakthrough is made possible through a creative use of sparse sampling theory and parallel imaging with phased array coils and a novel implementation of data acquisition and image reconstruction. We have successfully used the technique to perform 4D cardiovascular imaging on rats, achieving 0.65 mm × 0.65 mm × 0.31 mm spatial resolution with a frame rate of 67 fps. This capability enables simultaneous imaging of cardiac motion, respiratory motion, and first-pass myocardial perfusion. This in turn allows multiple cardiac assessments including measurement of ejection fraction, cardiac output, and myocardial blood flow in a single experiment. We believe that the proposed technique can open up many important applications of cardiovascular imaging and have significant impact on the field.
Joint use of partial separability (PS) and spatial-spectral sparsity constraints has previously been demonstrated useful for image reconstruction from undersampled data. This paper extends our early work in this area by proposing a new method for jointly enforcing the PS and spatial total variation (TV) constraints for dynamic MR image reconstruction. An algorithm is also described to solve the underlying optimization problem efficiently. The proposed method has been validated using simulated cardiac imaging data, with the expected capability to reduce image artifacts and reconstruction noise.
Real-time cardiac MRI is a very challenging problem because of limitations on imaging speed and resolution. To address this problem, the (k, t) - space MR signal is modeled as being partially separable along the spatial and temporal dimensions, which results in a rank-deficient data matrix. Image reconstruction is then formulated as a low-rank matrix recovery problem, which is solved using emerging low-rank matrix recovery techniques. In this paper, the Power Factorization algorithm is applied to efficiently recover the cardiac data matrix. Promising results are presented to demonstrate the performance of this novel approach.
The partially separable function (PSF) model has been successfully used to reconstruct cardiac MR images with high spatiotemporal resolution from sparsely sampled (k,t)-space data. However, the underlying model fitting problem is often ill-conditioned due to temporal undersampling, and image artifacts can result if reconstruction is based solely on the data consistency constraints. This paper proposes a new method to regularize the inverse problem using sparsity constraints. The method enables both partial separability (or low-rankness) and sparsity constraints to be used simultaneously for high-quality image reconstruction from undersampled (k,t)-space data. The proposed method is described and reconstruction results with cardiac imaging data are presented to illustrate its performance.
This paper presents an adaptive multigrid method used in both the forward and inverse problems. The proposed method combines adaptive mesh and multigrid solution strategy to resolve the forward problem. The accuracy and efficiency of the former forward solver are improved by incorporating the above two procedures. For image reconstruction the regularized Gauss-Newton method combined with adaptive multigrid method can improve the spatial resolution of reconstructed images. Both experimental and simulated results are presented.
Athinoula A. Martinos Center for Biomedical Imaging