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.

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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.

Magnetic resonance (MR) fingerprinting is a new quantitative imaging paradigm, which simultaneously acquires multiple MR tissue parameter maps in a single experiment. In this paper, we present an estimation-theoretic framework to perform experiment design for MR fingerprinting. Specifically, we describe a discrete-time dynamic system to model spin dynamics, and derive an estimation-theoretic bound, i.e., the Cramér-Rao bound (CRB), to characterize the signal-to-noise ratio (SNR) efficiency of an MR fingerprinting experiment. We then formulate an optimal experiment design problem, which determines a sequence of acquisition parameters to encode MR tissue parameters with the maximal SNR efficiency, while respecting the physical constraints and other constraints from the image decoding/reconstruction process. We evaluate the performance of the proposed approach with numerical simulations, phantom experiments, and in vivo experiments. We demonstrate that the optimized experiments substantially reduce data acquisition time and/or improve parameter estimation. For example, the optimized experiments achieve about a factor of two improvement in the accuracy of T2 maps, while keeping similar or slightly better accuracy of T1 maps. Finally, as a remarkable observation, we find that the sequence of optimized acquisition parameters appears to be highly structured rather than randomly/pseudorandomly varying as is prescribed in the conventional MR fingerprinting experiments.