Fast and accurate compensation of signal offset for T₂ mapping

T₂ maps are more vendor independent than other MRI protocols. Multi-echo spin-echo signal decays to a non-zero offset due to imperfect refocusing pulses and Rician noise, causing T₂ overestimation by the vendor's 2-parameter algorithm. The accuracy of the T₂ estimate is improved, if the non-zero offset is estimated as a third parameter. Three-parameter Levenberg-Marquardt (LM) T₂ estimation takes several minutes to calculate, and it is sensitive to initial values. We aimed for a 3-parameter fitting algorithm that was comparably accurate, yet substantially faster.

Our approach gains speed by converting the 3-parameter minimisation problem into an empirically unimodal univariate problem, which is quickly minimised using the golden section line search (GS).

To enable comparison, we propose a novel noise-masking algorithm. For clinical data, the agreement between the GS and the LM fit is excellent, yet the GS algorithm is two orders of magnitude faster. For synthetic data, the accuracy of the GS algorithm is on par with that of the LM fit, and the GS algorithm is significantly faster. The GS algorithm requires no parametrisation or initialisation by the user.

The new GS T₂ mapping algorithm offers a fast and much more accurate off-the-shelf replacement for the inaccurate 2-parameter fit in the vendor's software.