Quantitative MR Image Reconstruction Using Parameter-Specific Dictionary Learning With Adaptive Dictionary-Size and Sparsity-Level Choice

Objective:
We propose a method for the reconstruction of parameter-maps in Quantitative Magnetic Resonance Imaging (QMRI).
Methods:
Because different quantitative parameter-maps differ from each other in terms of local features, we propose a method where the employed dictionary learning (DL) and sparse coding (SC) algorithms automatically estimate the optimal dictionary-size and sparsity level separately for each parameter-map. We evaluated the method on a
$T_{1}$
-mapping QMRI problem in the brain using the BrainWeb data as well as in-vivo brain images acquired on an ultra-high field 7 T scanner. We compared it to a model-based acceleration for parameter mapping (MAP) approach, other sparsity-based methods using total variation (TV), Wavelets (Wl), and Shearlets (Sh) to a method which uses DL and SC to reconstruct qualitative images, followed by a non-linear (DL+Fit).
Results:
Our algorithm surpasses MAP, TV, Wl, and Sh in terms of RMSE and PSNR. It yields better or comparable results to DL+Fit by additionally significantly accelerating the reconstruction by a factor of approximately seven.
Conclusion:
The proposed method outperforms the reported methods of comparison and yields accurate
$T_{1}$
-maps. Although presented for
$T_{1}$
-mapping in the brain, our method's structure is general and thus most probably also applicable for the the reconstruction of other quantitative parameters in other organs.
Significance:
From a clinical perspective, the obtained
$T_{1}$
-maps could be utilized to differentiate between healthy subjects and patients with Alzheimer's disease. From a technical perspective, the proposed unsupervised method could be employed to obtain ground-truth data for the development of data-driven methods based on supervised learning.