Accelerating Magnetic Resonance T1ρ Mapping Using Simultaneously Spatial Patch-Based and Parametric Group-Based Low-Rank Tensors (SMART)

Quantitative magnetic resonance (MR) <inline-formula> <tex-math notation="LaTeX">$\text T_{{1}\rho }$ </tex-math></inline-formula> mapping is a promising approach for characterizing intrinsic tissue-dependent information. However, long scan time significantly hinders its widespread applications. Recently, low-rank tensor models have been employed and demonstrated exemplary performance in accelerating MR <inline-formula> <tex-math notation="LaTeX">$\text T_{{1}\rho }$ </tex-math></inline-formula> mapping. This study proposes a novel method that uses spatial patch-based and parametric group-based low-rank tensors simultaneously (SMART) to reconstruct images from highly undersampled k-space data. The spatial patch-based low-rank tensor exploits the high local and nonlocal redundancies and similarities between the contrast images in <inline-formula> <tex-math notation="LaTeX">$\text T_{{1}\rho }$ </tex-math></inline-formula> mapping. The parametric group-based low-rank tensor, which integrates similar exponential behavior of the image signals, is jointly used to enforce multidimensional low-rankness in the reconstruction process. In vivo brain datasets were used to demonstrate the validity of the proposed method. Experimental results demonstrated that the proposed method achieves 11.7-fold and 13.21-fold accelerations in two-dimensional and three-dimensional acquisitions, respectively, with more accurate reconstructed images and maps than several state-of-the-art methods. Prospective reconstruction results further demonstrate the capability of the SMART method in accelerating MR <inline-formula> <tex-math notation="LaTeX">$\text T_{{1}\rho }$ </tex-math></inline-formula> imaging.