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.
Athinoula A. Martinos Center for Biomedical Imaging