On Using Signal Magnitude in Diffusion Magnetic Resonance Measurements of Restricted Motion

Tissue microstructure has significance as a biomarker, however its accurate inference with diffusion magnetic resonance (MR) is still an open problem. With few exceptions, diffusion weighted (DW) MR models either process diffusion MR data using signal magnitude, whereby microstructural information is forcefully confined to symmetry due to Fourier transform properties, or directly use symmetric basis expansions. Herein, information loss from magnitude utilization is demonstrated by numerically simulating particles undergoing diffusion near a fully reflective infinite wall and an orthogonal corner. Simulation results show that the loss of the Hermitian property when using signal magnitude impedes DW--MR from accurately inferring microstructural information in both of the geometries.