MR Fingerprinting (MRF) is a novel fast imaging technique for simultaneous quantitative multi-parametric mappings¹. The original MRF maps were reconstructed by using a single spiral interleaf with variable TR& Flip angle (FA) and a pixel-wise template matching method. However, due to the inherent highly undersampling for each slice, the artifacts affect the final parametric mappings so that more than 1000 repetitions are needed for each slice acquisition in order to obtain robust results. To further accelerate the acquisition of MRF, a low rank and sparsity based MRF reconstruction scheme (L&S MRF) is proposed in this study for reducing the artifacts at each time point within a fraction of acquisition times used in the original MRF¹.

For L time points, define M=[M₁, M₂, …, M_L,] as the spiral k-space data matrix measured from L spiral interleaves, and x as the reconstructed image series, in which the individual image has N pixels. The L&S MRF method utilizes both the low rank and sparsity constraint² on the acquired data for reconstruction, which can be expressed by:$$ \bf {\widehat{X}}=argmin\parallel\bf{FX-M}\parallel _2^2+\lambda_{\it L}\parallel \bf{X}\parallel _*+\lambda_{\it S}\parallel {\varPsi}\bf{X}\parallel _1,\qquad [1]$$where X (with size N*L) is the Casorati matrix that is rearranged from the image series x, F is the non-uniform FFT operator, and Ψ is the sparse transform operator that act on each column of X. λ_L and λ_S are the regularization parameters that can be tuned for optimizations.Both low rank and sparsity constraint are exploited in Eq. [1]. First, the low rank constraint is based on the assumption of high correlations of images between interleaves, and it can be enforced for all time points with the same background. Second, the joint sparsity constraint is exploited with the assumption that the sparsity of different contrast-weighted images between interleaves (induced by variable TRs/FAs in MRF acquisitions) is highly correlated. Figure 1 shows the flowchart of our proposed reconstruction scheme. This reconstruction is iterated until the preset tolerance value (10^-3 in this study) is achieved, and then the reconstructed images from all time points are used for template matching.

In vivo brain experiment was performed for validation on a 3T scanner (MAGNETOM Prisma, Siemens Healthcare, Erlangen, Germany) with 20-channel head coil. The MRF sequence was based on an inversion-prepared FISP sequence³ with TR varying from 10 to 12ms, FA varying from 5 to 80 degrees, and a variable density spiral trajectory rotating 12 degrees for each TR. The dictionary was based on the extended phase graph algorithm⁴ with the range of T1 from 20 to 6000ms and T2 from 20 to 3000ms. For L&S MRF reconstruction, Ψ was selected as the spatial Fourier transform operator, λ_L = 0.005 and λ_S =0.001 which were tuned for least normalized sum-of-square error (NSSE). The proposed L&S MRF method was also compared with original MRF method using the same dataset with the number of time points L=600. The reference parametric mappings were obtained by original MRF method with the number of time points L=3000.

Figure 2 shows the T1, T2 and proton density maps of reference, original MRF and our proposed method. It can be seen that when L=600, our proposed method is robust against the noise, and has smaller NSSE than original method (0.0131 vs 0.0235 for T1 map, 0.0260 vs 0.0918 for T2 map and 0.0225 vs 0.1639 for proton density map, respectively).Compared with original pixel-wise reconstruction scheme, high correlations between interleaves (low rank constraint enforced) and pixels (sparsity constraint enforced) are exploited as the prior information in our proposed L&S method, to reach for better performance of reconstructions. Since the results of original MRF method are affected by artifacts due to highly under-sampling, L&S MRF method utilizing simultaneous low rank and sparsity structures reduces the artifacts, thus the number of time points can be decreased for acceleration.