Due to their extreme noise amplification, current Quantitative Conductivity Mapping (QCM) techniques require high SNR images. Simultaneous Quantitative Susceptibility Mapping and QCM uses low-SNR gradient-echo sequences, creating a need for QCM methods appropriate for noisy images. Here we proposed, optimised, and compared several new QCM methods (all shared on https://xip.uclb.com/i/software/MRI_conductivity.html) built on the widely-used phase-based formula and its equivalent, less popular integral form. We found that solving the integral equation provided lower errors and better edge preservation in both simulated and in-vivo images, and that edge preservation combining magnitude-based and image-segmentation-based techniques resulted in the best in-vivo conductivity map.
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