Iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL): application with fast spin-echo imaging

Chemical shift based methods are often used to achieve uniform water-fat separation that is insensitive to Bo inhomogeneities. Many spin-echo (SE) or fast SE (FSE) approaches acquire three echoes shifted symmetrically about the SE, creating time-dependent phase shifts caused by water-fat chemical shift. This work demonstrates that symmetrically acquired echoes cause artifacts that degrade image quality. According to theory, the noise performance of any water-fat separation method is dependent on the proportion of water and fat within a voxel, and the position of echoes relative to the SE. To address this problem, we propose a method termed "iterative decomposition of water and fat with echo asymmetric and least-squares estimation" (IDEAL). This technique combines asymmetrically acquired echoes with an iterative least-squares decomposition algorithm to maximize noise performance. Theoretical calculations predict that the optimal echo combination occurs when the relative phase of the echoes is separated by 2pi/3, with the middle echo centered at pi/2+pik (k=any integer), i.e., (-pi/6+pik, pi/2+pik, 7pi/6+pik). Only with these echo combinations can noise performance reach the maximum possible and be independent of the proportion of water and fat. Close agreement between theoretical and experimental results obtained from an oil-water phantom was observed, demonstrating that the iterative least-squares decomposition method is an efficient estimator.