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

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.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.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.The relative l2 -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.Our proposed CC-IC-LMEN method provides accurate and robust solutions for accelerated MR T1rho mapping.