Improved estimation of MR relaxation parameters using complex-valued data

Purpose: In MR image analysis, T ₁, T ₂, and T ^* ₂ maps are generally calculated using magnitude MR data. Without knowledge of the underlying noise variance, parameter estimates at low signal to noise ratio (SNR) are usually biased. This leads to confounds in studies that compare parameters across SNRs and or across scanners. This article compares several estimation techniques which use real or complex-valued MR data to achieve unbiased estimation of MR relaxation parameters without the need for additional preprocessing. Theory and Methods: Several existing and new techniques to estimate relaxation parameters using complex-valued data were compared with widely used magnitude-based techniques. Their bias, variance and processing times were studied using simulations covering various aspects of parameter variations. Validation on noise-degraded experimental measurements was also performed. Results: Simulations and experiments demonstrated the superior performance of techniques based on complex-valued data, even in comparison with magnitude-based techniques that account for Rician noise characteristics. This was achieved with minor modifications to data modeling and at computational costs either comparable to or higher (≈ two fold) than magnitude-based estimators. Theoretical analysis shows that estimators based on complex-valued data are statistically efficient. Conclusion: The estimation techniques that use complex-valued data provide minimum variance unbiased estimates of parametric maps and markedly outperform commonly used magnitude-based estimators under most conditions. They additionally provide phase maps and field maps, which are unavailable with magnitude-based methods. Magn Reson Med 77:385–397, 2017.