Characteristic-constrained accelerating MR T1rho mapping with blockwise infimal convolution of matrix elastic-net regularization.

Background: Magnetic resonance parameter mapping (MRPM) plays an important role in clinical applications and biomedical researches. However, the acceleration of MRPM remains a major challenge for achieving further improvements.

Purpose: In this work, a new undersampled k-space based joint multi-contrast image reconstruction approach named CC-IC-LMEN is proposed for accelerating MR T1rho mapping.

Methods: The reconstruction formulation of the proposed CC-IC-LMEN method imposes a blockwise low-rank assumption on the characteristic-image series (c-p space) and utilizes infimal convolution (IC) to exploit and balance the generalized low-rank properties in low-and high-order c-p spaces, thereby improving the accuracy. In addition, matrix elastic-net (MEN) regularization based on the nuclear and Frobenius norms is incorporated to obtain stable and exact solutions in cases with large accelerations and noisy observations. This formulation results in a minimization problem, that can be effectively solved using a numerical algorithm based on the alternating direction method of multipliers (ADMM). Finally, T1rho maps are then generated according to the reconstructed images using nonlinear least-squares (NLSQ) curve fitting with an established relaxometry model.

Results: The relative l -norm error (RLNE) and structural similarity (SSIM) in the regions of interest (ROI) show that the CC-IC-LMEN approach is more accurate than other competing methods even in situations with heavy undersampling or noisy observation.

Conclusions: Our proposed CC-IC-LMEN method provides accurate and robust solutions for accelerated MR T1rho mapping.