Abstract #0027

Fast Unwrapping using Discrete Gradient Evaluation (FUDGE): an analytical correction to the Laplacian-based phase unwrapping technique for discrete data.

Amanda Ching Lih Ng¹, Meei Pyng Ng², Sonal Josan³, Shawna Farquharson⁴, Claire Mulcahy⁴, and Roger J Ordidge¹

¹Dept of Anatomy & Neuroscience, The University of Melbourne, Parkville, Australia, ²Dept of Mathematics & Statistics, The University of Melbourne, Parkville, Australia, ³Siemens Healthcare, Melbourne, Australia, ⁴Imaging, The Florey Institute of Neuroscience and Mental Health, Melbourne, Australia

Laplacian-based phase unwrapping is commonly used to pre-process phase for methods such as Quantitative Susceptibility Mapping (QSM). However, the formulation was derived with the assumption of a continuous signal and a continuous Fourier transform. When applied to discrete MRI phase data, serious errors in phase can occur, resulting in substantial errors in QSM estimates. We present a mathematically correct Laplacian-based phase unwrapping formula, based on the assumption of the discrete nature of MRI phase data and processing. Our results reflect the mathematical predictions of the old and new formulations.

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