A convex relaxation approach to fat/water separation with minimum label description

While Magnetic Resonance Imaging is capable of separating water and fat components in the body, mapping of magnetic field inhomogeneities is essential for the successful application of this process. In this study, we address the problem of field map estimation using a convex-relaxed max-flow method. We propose a novel two-stage approach that leads to the global optimum of the proposed problem. The first stage minimizes the signal residuals via a convex-relaxed minimum description length (MDL)-based approach. The MDL-based labeling model penalizes the total number of appearing labels, which helps to avoid field map errors when abrupt changes in field homogeneity exist. By exploringthe whole range of possible frequency offsets, this stage ensures limiting the estimated field offset within certain boundaries where the global minimum resides. The second stage employs the output of the labeling model in a commonly used gradient-descent based method (known as IDEAL) to converge to the exact global minimum, i.e. the required value of the field offset. Experimental results for cardiac imaging, where challenging field inhomogeneities exist, showed that our method significantly outperforms over a widely-used technique for fat/water separation in terms of robustness and efficiency.