Objective: To visualize the encoding capability of magnetic resonance fingerprinting (MRF) dictionaries. Materials and methods: High-dimensional MRF dictionaries were simulated and embedded into a lower-dimensional space using t-distributed stochastic neighbor embedding (t-SNE). The embeddings were visualized via colors as a surrogate for location in low-dimensional space. First, we illustrate this technique on three different MRF sequences. We then compare the resulting embeddings and the color-coded dictionary maps to these obtained with a singular value decomposition (SVD) dimensionality reduction technique. We validate the t-SNE approach with measures based on existing quantitative measures of encoding capability using the Euclidean distance. Finally, we use t-SNE to visualize MRF sequences resulting from an MRF sequence optimization algorithm. Results: t-SNE was able to show clear differences between the color-coded dictionary maps of three MRF sequences. SVD showed smaller differences between different sequences. These findings were confirmed by quantitative measures of encoding. t-SNE was also able to visualize differences in encoding capability between subsequent iterations of an MRF sequence optimization algorithm. Discussion: This visualization approach enables comparison of the encoding capability of different MRF sequences. This technique can be used as a confirmation tool in MRF sequence optimization.

Quality assessment of different Magnetic Resonance Fingerprinting (MRF) sequences and their corresponding dictionaries remains an unsolved problem. In this work we present a method in which we approach analysis of MRF dictionaries by performing dimensionality reduction and representing them as low-dimensional point sets (embeddings). Dimensionality reduction was performed using a modification of the t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm. First, we demonstrated stability of calculated embeddings that allows neglecting the stochastic nature of t-SNE. Next, we proposed and analyzed two algorithms for comparing the embeddings. Finally, we performed two simulations in which we reduced the MRF sequence/dictionary in length or size and analyzed the influence of this reduction on the resulting embedding. We believe that this research can pave the way to development of a software tool for analysis, including better understanding, optimization and comparison, of different MRF sequences.

Purpose: Design of a preconditioner for fast and efficient parallel imaging (PI) and compressed sensing (CS) reconstructions for Cartesian trajectories. Theory: PI and CS reconstructions become time consuming when the problem size or the number of coils is large, due to the large linear system of equations that has to be solved in l₁ and l₂-norm based reconstruction algorithms. Such linear systems can be solved efficiently using effective preconditioning techniques. Methods: In this article we construct such a preconditioner by approximating the system matrix of the linear system, which comprises the data fidelity and includes total variation and wavelet regularization, by a matrix that is block circulant with circulant blocks. Due to this structure, the preconditioner can be constructed quickly and its inverse can be evaluated fast using only two fast Fourier transformations. We test the performance of the preconditioner for the conjugate gradient method as the linear solver, integrated into the well-established Split Bregman algorithm. Results: The designed circulant preconditioner reduces the number of iterations required in the conjugate gradient method by almost a factor of 5. The speed up results in a total acceleration factor of approximately 2.5 for the entire reconstruction algorithm when implemented in MATLAB, while the initialization time of the preconditioner is negligible. Conclusion: The proposed preconditioner reduces the reconstruction time for PI and CS in a Split Bregman implementation without compromising reconstruction stability and can easily handle large systems since it is Fourier-based, allowing for efficient computations.