HDNLS: Hybrid Deep Learning and Non-linear Least Squares-based Method for Fast Multi-Component T1$$$\rho$$$ Mapping in the Knee Joint

Motivation: Non-linear least squares (NLS)-based T1$$$\rho$$$ fitting converges slowly and sensitive to initial guesses. Deep learning-based methods offer efficient alternatives, but suffer from overfitting and generalization problems. Goal(s): To overcome the limitations of NLS and DL, we introduce HDNLS, which uses DL-based T1ρ fitting as an initial guess for NLS. Approach: The optimal number of NLS iterations is determined by analyzing the trade-off between precision and fitting time. Finally, four HDNLS variants are suggested: Ultrafast-HDNLS, Superfast-HDNLS, HDNLS, and Relaxed-HDNLS. Results: HDNLS exhibits similar behavior to NLS and Regularized NLS (RNLS) with a minimum of 13-times increase in fitting speed. Impact: Our results indicate that HDNLS is faster and exhibits similar behavior to NLS for whole knee joint T1$$$\rho$$$ mapping than NLS. Thus, HDNLS is an alternative to replace NLS and RNLS for T1$$$\rho$$$ mapping when computational time is an issue.