MODEL-BASED MR PARAMETER MAPPING WITH SPARSITY CONSTRAINT

Improved magnetic resonance fingerprinting reconstruction with low-rank and subspace modeling

PURPOSE

This article introduces a constrained imaging method based on low-rank and subspace modeling to improve the accuracy and speed of MR fingerprinting (MRF).

THEORY AND METHODS

A new model-based imaging method is developed for MRF to reconstruct high-quality time-series images and accurate tissue parameter maps (e.g., T₁ , T₂ , and spin density maps). Specifically, the proposed method exploits low-rank approximations of MRF time-series images, and further enforces temporal subspace constraints to capture magnetization dynamics. This allows the time-series image reconstruction problem to be formulated as a simple linear least-squares problem, which enables efficient computation. After image reconstruction, tissue parameter maps are estimated via dictionary-based pattern matching, as in the conventional approach.

RESULTS

The effectiveness of the proposed method was evaluated with in vivo experiments. Compared with the conventional MRF reconstruction, the proposed method reconstructs time-series images with significantly reduced aliasing artifacts and noise contamination. Although the conventional approach exhibits some robustness to these corruptions, the improved time-series image reconstruction in turn provides more accurate tissue parameter maps. The improvement is pronounced especially when the acquisition time becomes short.

CONCLUSIONS

The proposed method significantly improves the accuracy of MRF, and also reduces data acquisition time. Magn Reson Med 79:933-942, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Trust Region Methods for the Estimation of a Complex Exponential Decay Model in MRI With a Single-Shot or Multi-Shot Trajectory

Joint estimation of spin density R2* decay and OFF-resonance frequency maps is very useful in many magnetic resonance imaging applications. The standard multi-echo approach can achieve high accuracy but requires a long acquisition time for sampling multiple k-space frames. There are many approaches to accelerate the acquisition. Among them, single-shot or multi-shot trajectory-based sampling has recently drawn attention due to its fast data acquisition. However, this sampling strategy destroys the Fourier relationship between k-space and images, leading to a great challenge for the reconstruction. In this paper, we present two trust region methods based on two different linearization strategies for the nonlinear signal model. A trust region is defined as a local area in the variable space where a local linear approximation is trustable. In each iteration, the method minimizes a local approximation within a trust region so that the step size can be kept in a suitable scale. A continuation scheme is applied to reduce the regularization gradually over the parameter maps and facilitates convergence from poor initializations. The two trust region methods are compared with the two other previously proposed methods--the nonlinear conjugate gradients and the gradual refinement algorithm. Experiments based on various synthetic data and real phantom data show that the two trust region methods have a clear advantage in both speed and stability.

Model-based MR parameter mapping with sparsity constraints: parameter estimation and performance bounds

Magnetic resonance parameter mapping (e.g., T1 mapping, T2 mapping, 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. 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.

PANDA-T1ρ: Integrating principal component analysis and dictionary learning for fast T1ρ mapping

PURPOSE

Long scanning time greatly hinders the widespread application of spin-lattice relaxation in rotating frame (T1ρ) in clinics. In this study, a novel method is proposed to reconstruct the T1ρ-weighted images from undersampled k-space data and hence accelerate the acquisition of T1ρ imaging.

METHODS

The proposed approach (PANDA-T1ρ) combined the benefit of PCA and dictionary learning when reconstructing image from undersampled data. Specifically, the PCA transform was first used to sparsify the image series along the parameter direction and then the sparsified images were reconstructed by means of dictionary learning and finally solved the images. A variation of PANDA-T1ρ was also developed for the heavy noise case. Numerical simulation and in vivo experiments were carried out with the accelerating factor from 2 to 4 to verify the performance of PANDA-T1ρ.

RESULTS

The reconstructed T1ρ maps using the PANDA-T1ρ method were found to be comparable to the reference at all verified acceleration factors. Moreover, the variation exhibited better performance than the original version when the k-space data were contaminated by heavy noise.

CONCLUSION

PANDA-T1ρ can significantly reduce the scanning time of T1ρ by integrating PCA and dictionary learning and provides better parameter estimation than the state-of-art methods for a fixed acceleration factor.