Fast and accurate compensation of signal offset for T2 mapping

  • Jan MichálekEmail author
  • Pavla Hanzlíková
  • Tuan Trinh
  • Dalibor Pacík
Research Article



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.


Algorithms Least-squares analysis Software 



We acknowledge the core facility MAFIL of CEITEC, which was supported by the Czech BioImaging large RI project (LM2015062 funded by MEYS CR), for their support with obtaining the scientific data that were presented in this paper. The corresponding author also appreciates the valuable discussions on the theoretical aspects of the algorithm with M. Kozubek from the Centre for Biomedical Image Analysis, Faculty of Informatics, Masaryk University, as well as his comments that helped streamline the manuscript.

Authors' contributions

JM: Study conception and design, analysis and interpretation of data, drafting the manuscript, PH: Analysis and interpretation of data, DP: Acquisition of data, TT: Acquisition of data.


This work was supported by the Czech BioImaging large infrastructure project (LM2015062 funded by MEYS CR).

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest to disclose.

Ethical approval

All procedures that were performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed consent

Informed consent was obtained from all individual participants that were included in the study.

Code availability

The MATLAB code for the algorithm described in this paper is available at

Supplementary material

10334_2019_737_MOESM1_ESM.docx (1.7 mb)
Supplementary file1 (DOCX 1690 kb)


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Copyright information

© European Society for Magnetic Resonance in Medicine and Biology (ESMRMB) 2019

Authors and Affiliations

  1. 1.Centre for Biomedical Image Analysis, Faculty of InformaticsMasaryk UniversityBrnoCzech Republic
  2. 2.Department of Radiology, Faculty of Medicine and DentistryPalacky UniversityOlomoucCzech Republic
  3. 3.Department of Urology, Medical SchoolMasaryk UniversityBrnoCzech Republic
  4. 4.Department of UrologyUniversity Hospital BrnoBrnoCzech Republic

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