Phase unwrapping with a rapid opensource minimum spanning tree algorithm (ROMEO).

Barbara Dymerska,Beata Bachrata,Korbinian Eckstein,Karin Shmueli,Bernard Siow,Simon Daniel Robinson,Siegfried Trattnig

doi:10.1002/mrm.28563

Abstract

PurposeTo develop a rapid and accurate MRI phase‐unwrapping technique for challenging phase topographies encountered at high magnetic fields, around metal implants, or postoperative cavities, which is sufficiently fast to be applied to large‐group studies including Quantitative Susceptibility Mapping and functional MRI (with phase‐based distortion correction).MethodsThe proposed path‐following phase‐unwrapping algorithm, ROMEO, estimates the coherence of the signal both in space—using MRI magnitude and phase information—and over time, assuming approximately linear temporal phase evolution. This information is combined to form a quality map that guides the unwrapping along a 3D path through the object using a computationally efficient minimum spanning tree algorithm. ROMEO was tested against the two most commonly used exact phase‐unwrapping methods, PRELUDE and BEST PATH, in simulated topographies and at several field strengths: in 3T and 7T in vivo human head images and 9.4T ex vivo rat head images.ResultsROMEO was more reliable than PRELUDE and BEST PATH, yielding unwrapping results with excellent temporal stability for multi‐echo or multi‐time‐point data. It does not require image masking and delivers results within seconds, even in large, highly wrapped multi‐echo data sets (eg, 9 seconds for a 7T head data set with 31 echoes and a 208 × 208 × 96 matrix size).ConclusionOverall, ROMEO was both faster and more accurate than PRELUDE and BEST PATH, delivering exact results within seconds, which is well below typical image acquisition times, enabling potential on‐console application.

Highlights

The complex signal in MRI can be divided into two constituents: magnitude (M) and phase (θ)
Path-following algorithms compare the phase in adjacent voxels, beginning at one location and proceeding to neighboring voxels in an order dictated by the reliability of the information in the voxels and how well they are connected
We have presented a new, rapid, and robust phase unwrapping technique—ROMEO—that is more reliable and faster than the two exact phase-unwrapping algorithms most commonly used in MRI: PRELUDE and BEST PATH

Summary

| INTRODUCTION

The complex signal in MRI can be divided into two constituents: magnitude (M) and phase (θ). Laplacian unwrapping is the most robust method currently available, providing globally smooth phase results (ie, no abrupt jumps) within seconds, even for large data sets with low SNR, explaining its popularity in QSM It does not yield exact results for θ,11 which makes it unsuitable for applications such as distortion correction, flow, or temperature measurements (see Supporting Information Figure S1). To overcome the shortcomings of the exact phase-unwrapping algorithms currently available, we propose a new path-following algorithm called ROMEO: Rapid Opensource Minimum spanning treE algOrithm This algorithm (1) uses up to three measures of the quality of connections between voxels, or weights, calculated from phase and magnitude information to provide improved unwrapping paths compared with BEST PATH, (2) provides computationally efficient bookkeeping of quality values and respective voxel edges, and (3) offers single-step unwrapping of a fourth dimension (echo or time). Source code in the Julia[19] programming language, compiled versions for Linux and Windows ( executable using command line or MATLAB [MathWorks, Natick, MA]) and the data sets used in this study are publicly available (see Data Availability Statement)

| METHODS

Magnitude Coherence weight

| RESULTS

Findings

| DISCUSSION

| CONCLUSIONS