To propose and evaluate a new model-based reconstruction method for highly accelerated phase-contrast magnetic resonance imaging (PC-MRI) with sparse sampling.
Theory and Methods
This work presents a new constrained reconstruction method based on low-rank and sparsity constraints to accelerate PC-MRI. More specifically, we formulate the image reconstruction problem into separate reconstructions of flow-reference image sequence and complex differences. We then utilize the joint partial separability and sparsity constraints to enable high quality reconstruction from highly undersampled -space data. We further integrate the proposed method with ESPIRiT based parallel imaging model to effectively handle multichannel acquisition.
The proposed method was evaluated with in vivo data acquired from both 2D and 3D PC flow imaging experiments, and compared with several state-of-the-art methods. Experimental results demonstrate that the proposed method leads to more accurate velocity reconstruction from highly undersampled -space data, and particularly superior capability of capturing the peak velocity of blood flow. In terms of flow visualization, blood flow patterns obtained from the proposed reconstruction also exhibit better agreement with those obtained from the fully sampled reference.
The proposed method achieves improved accuracy over several state-of-the-art methods for velocity reconstruction with highly accelerated -space data.
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 MR tissue 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, 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.
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.
Magnetic resonance parameter mapping (e.g., T1 mapping, T2 mapping, T2* 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. The proposed method utilizes a formulation that integrates the explicit signal model with sparsity constraints on the model parameters, enabling direct estimation of the parameters of interest from highly undersampled, noisy k-space data. An efficient greedy-pursuit algorithm is described to solve the resulting constrained parameter estimation problem. Estimation-theoretic bounds are also derived to analyze the benefits of incorporating sparsity constraints and benchmark the performance of the proposed method. The theoretical properties and empirical performance of the proposed method are illustrated in a T2 mapping application example using computer simulations.
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. In this paper, we present a novel method to accelerate cardiovascular MRI through the integration of parallel imaging, low-rank modeling, and sparse modeling. This method consists of a novel image model and specialized data acquisition. Of particular novelty is the proposed low-rank model component, which is specially adapted to the particular low-rank structure of cardiovascular signals. Simulations and in vivo experiments were performed to evaluate the method, as well as an analysis of the low-rank structure of a numerical cardiovascular phantom. Cardiac imaging experiments were carried out on both human and rat subjects without the use of ECG or respiratory gating and without breath holds. The proposed method reconstructed 2-D human cardiac images up to 22 fps and 1.0 mm × 1.0 mm spatial resolution and 3-D rat cardiac images at 67 fps and 0.65 mm × 0.65 mm × 0.31 mm spatial resolution. These capabilities will enhance the practical utility of cardiovascular MRI.
Partial separability (PS) and sparsity have been previously used to enable reconstruction of dynamic images from undersampled (k, t)-space data. This paper presents a new method to use PS and sparsity constraints jointly for enhanced performance in this context. The proposed method combines the complementary advantages of PS and sparsity constraints using a unified formulation, achieving significantly better reconstruction performance than using either of these constraints individually. A globally convergent computational algorithm is described to efficiently solve the underlying optimization problem. Reconstruction results from simulated and in vivo cardiac MRI data are also shown to illustrate the performance of the proposed method.
Electrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution inside an inhomogeneous distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. A hybrid method is proposed for solving the inverse problem for EIT, which combines the Krylov subspace and the Tikhonov regularization for double levels of regularization to the ill-posed problem. Numerical simulation results using the hybrid method are presented and compared to those from truncated singular value decomposition (TSVD) regularization and the Tikhonov regularization. Experimental results with the hybrid method are also presented, indicating that the hybrid method can reduce the computation time, and improve the resolution of reconstructed images with the regularization parameter automatically chosen by the L-curve method.
lectrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution of an inhomogeneous medium, usually by injecting a current at the periphery of an object and measuring the resulting changes in voltage. The conjugate gradient (CG) method is one of the most popular methods applied for image reconstruction, although its convergence rate is low. In this paper, an advanced version of the CG method, i.e. the Schur conjugate gradient (Schur CG) method, is used to solve the inverse problem for EIT. The solution space is divided into two subspaces. The main part of the solution lies in the coarse subspace, which can be calculated directly and its corresponding correction term with a small norm can be solved in the Schur complement subspace. This paper discusses the strategies of choosing parameters. Simulation results using the Schur CG algorithm are presented and compared with the conventional CG algorithm. Experimental results obtained by the Schur CG algorithm are also presented, indicating that the Schur CG algorithm can reduce the computational time and improve the quality of image reconstruction with the selected parameters.
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