A modified Fourier-based phase unwrapping algorithm with an application to MRI venography

Purpose: To present a single-step deterministic procedure for unwrapping MRI phase maps. Materials and Methods: Using an algorithm previously developed for optical applications, Laplacian operators were applied in the Fourier space of the MRI phase map. The original Fourier-based phase unwrapping algorithm was modified so that demodulation accomplished the required signal symmetrization in Fourier space. To evaluate the method's performance in the presence of thermal noise, a set of wrapped phase maps were simulated at different levels of noise in k-space, and the response of the algorithm at different levels of signal-to-noise ratio (SNR) was evaluated for stability. To demonstrate its utility in MRI, the algorithm was applied to the wrapped phase maps of susceptibility-weighted imaging (SWI) studies, which were then used to generate venograms. Results: In simulated phase wrapping, the algorithm correctly reproduced the original phase for a wide range of phase gradients and noise. The procedure was fast and produced useful maps of venous structures in SWI images. Conclusion: A fast and stable single-step deterministic method for unwrapping MRI phase maps is available for such applications as SWI and mapping of static magnetic field inhomogeneity.