Improving subspace constrained radial fast spin echo MRI using block matching driven non-local low rank regularization

Abstract

Subspace-constrained reconstruction methods restrict the relaxation signals (of size M) in the scene to a pre-determined subspace (of size K≪M) and allow multi-contrast imaging and parameter mapping from accelerated acquisitions. However, these constraints yield poor image quality at some imaging contrasts, which can impact the parameter mapping performance. Additional regularization such as the use of joint-sparse (JS) or locally-low-rank (LLR) constraints can help improve the recovery of these images but are not sufficient when operating at high acceleration rates. We propose a method, non-local rank 3D (NLR3D), that is built on block matching and transform domain low rank constraints to allow high quality recovery of subspace-coefficient images (SCI) and subsequent multi-contrast imaging and parameter mapping. The performance of NLR3D was evaluated using Monte-Carlo (MC) simulations and compared against the JS and LLR methods. In vivo T ₂ mapping results are presented on brain and knee datasets. MC results demonstrate improved bias, variance, and MSE behavior in both the multi-contrast images and parameter maps when compared to the JS and LLR methods. In vivo brain and knee results at moderate and high acceleration rates demonstrate improved recovery of high SNR early TE images as well as parameter maps. No significant difference was found in the T2 values measured in ROIs between the NLR3D reconstructions and the reference images (Wilcoxon signed rank test). The proposed method, NLR3D, enables recovery of high-quality SCI and, consequently, the associated multi-contrast images and parameter maps.

Figure 1:

(A) Subspace-constraint enforced on a sequence of contrast weighted images. (B) The truncated subspace basis and the corresponding subspace-coefficient images are shown, with 3D patch matching on the subspace-coefficient images. (C) For a reference 3D patch, distinguished by the letter R in the center of the patch (and colored in red), the top L nearest 3D patches are identified, and the sequence of operations in NLR3D are shown.

Figure 2:

Results of MC study for all the methods at R=16 for a single noise realization. Red arrows highlight areas on TE1 and T2 maps where JS and LLR methods are suboptimal.

Figure 3:

Normalized error maps from the Monte-Carlo study for all the reconstruction methods at R=16. The results in (A) correspond to the TE1 (heavier proton density weighting) images. The results in (B) correspond to the TE8 (heavier T₂ weighting) images. The results in (C) represent the error maps for the T₂ results. The T₂ NRMSE of different brain regions are shown in (D).

Figure 4:

Subspace-coefficient images recovered from the different reconstruction methods at R=16 for the in-vivo brain and knee datasets. Note that all methods perform comparably in recovering SCI-1 and SCI-2. The JS and LLR methods exhibit poor recovery of SCI-3 and SCI-4 in contrast to the NLR3D method.

Figure 5:

In-vivo brain results at R=8 and 16. TE1, TE8 and T₂ maps from all the reconstructions are shown. NMSE values, evaluated after setting the background, scalp, and skull regions to zero, are reported on the bottom right corner of each figure panel. Red arrows show areas where JS and LLR exhibit inferior performance.

Figure 6:

In-vivo knee results at R=8 and 16. TE1, TE5 and T₂ maps from all the reconstructions are shown. NMSE values, evaluated in the knee cartilage, are reported on the bottom right corner. Red arrows show areas where JS and LLR exhibit inferior performance.