Purpose: To enable accurate 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. Results: 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. Conclusions: Simultaneously imposing low-rank and sparsity constraints can effectively improve the accuracy of fast MR parameter mapping with sparse sampling.

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Purpose To accelerate spectroscopic imaging using sparse sampling of (k, t)-space and subspace (or low-rank) modeling to enable high-resolution metabolic imaging with good signal-to-noise ratio (SNR). Methods The proposed method, called SPICE (SPectroscopic Imaging by exploiting spatiospectral CorrElation), exploits a unique property known as partial separability of spectroscopic signals. This property indicates that high-dimensional spectroscopic signals reside in a very low-dimensional subspace and enables special data acquisition and image reconstruction strategies to be used to obtain high-resolution spatiospectral distributions with good SNR. More specifically, a hybrid CSI/EPSI pulse sequence is proposed for sparse sampling of (k, t)-space, and a low-rank model-based algorithm is proposed for subspace estimation and image reconstruction from sparse data with the capability to incorporate prior information and field inhomogeneity correction. Results The performance of SPICE has been evaluated using both computer simulations and phantom studies, which produced very encouraging results. For 2D spectroscopic imaging experiments on a metabolite phantom, a factor of 10 acceleration was achieved with a minimal loss in SNR compared to the long CSI experiments and with a significant gain in SNR compared to the accelerated EPSI experiments. Conclusion SPICE is able to significantly accelerate spectroscopic imaging experiments, making high-resolution metabolic imaging possible.

Purpose To develop data acquisition and image reconstruction methods to enable high-resolution 1H MR spectroscopic imaging (MRSI) of the brain, using the recently proposed subspace-based spectroscopic imaging framework called SPICE (SPectroscopic Imaging by exploiting spatiospectral CorrElation). Theory and Methods SPICE is characterized by the use of a subspace model for both data acquisition and image reconstruction. For data acquisition, we propose a novel spatiospectral encoding scheme that provides hybrid data sets for determining the subspace structure and for image reconstruction using the subspace model. More specifically, we use a hybrid chemical shift imaging (CSI)/echo-planar spectroscopic imaging (EPSI) sequence for two-dimensional (2D) MRSI and a dual-density, dual-speed EPSI sequence for three-dimensional (3D) MRSI. For image reconstruction, we propose a method that can determine the subspace structure and the high-resolution spatiospectral reconstruction from the hybrid data sets generated by the proposed sequences, incorporating field inhomogeneity correction and edge-preserving regularization. Results Phantom and in vivo brain experiments were performed to evaluate the performance of the proposed method. For 2D MRSI experiments, SPICE is able to produce high SNR spatiospectral distributions with an approximately 3 mm nominal in-plane resolution from a 10-min acquisition. For 3D MRSI experiments, SPICE is able to achieve an approximately 3 mm in-plane and 4 mm through-plane resolution in about 25 min. Conclusion Special data acquisition and reconstruction methods have been developed for high-resolution 1H-MRSI of the brain using SPICE. Using these methods, SPICE is able to produce spatiospectral distributions of 1H metabolites in the brain with high spatial resolution, while maintaining a good SNR. These capabilities should prove useful for practical applications of SPICE.

MR 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 times. 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.