In vivo proton MR images contain signals from water and fat protons. Separation of the water and fat signals is a problem of considerable practical importance. In some cases, the fat signal is of diagnostic interest (1–3), and in other circumstances it appears bright and obscures the water signal (4). A number of methods have been developed to address the water/fat separation problem. A straightforward approach is to suppress the fat signal during excitation, which can be done using fat saturation or spatial-spectral pulses (based on the difference in the resonance frequencies of water and fat protons) (5, 6), or by signal nulling using a short-tau inversion recovery sequence (based on the short *T*_{1} relaxation time of the fat signal) (7). However, fat suppression has well-known limitations, e.g., high sensitivity to amplitude of static field and amplitude of radio frequency field inhomogeneities, removal of fat signal information, or loss of signal-to-noise ratio (1, 4, 8).

An alternative is to separate the water and fat components by postprocessing chemical shift-encoded data, which is the crux of the celebrated Dixon method (9) and its many variants. In a chemical shift–based water/fat separation acquisition, a sequence of images is obtained with different echo time (TE) shifts, *t*_{1}, *t*_{2}, … , *t*_{N} (typically *N* = 3). The signal at an individual voxel *q* can be described by the simplified model:

where *f*_{B,q} (in hertz) is the local frequency shift due to static field inhomogeneity, ρ_{W,q} and ρ_{F,q} are the amplitudes of the water and fat components, respectively, and *f*_{F} (in hertz) is the frequency shift of fat relative to the water, which is assumed to be known a priori (4, 9, 10). In this simplified model, *T* effects are ignored and the fat signal is considered to have a single spectral line (11, 12). These simplifications can be removed if needed, as described in the Materials and Methods section.

The unknowns in the signal model of Eq. [1] are the nonlinear parameter *f*_{B,q} and the linear parameters ρ_{W,q}, ρ_{F,q}, for *q* = 1,…,*Q*, where *Q* is the number of voxels. Clearly, estimation of {ρ_{W,q}, ρ_{F,q}} is trivial if *f*_{B,q} is known. However, estimation of *f*_{B,q} is complicated by the nonlinearity of the signal model. Several practical factors make the problem even more challenging, including the large range of *f*_{B,q}, rapid spatial variation of *f*_{B,q}, presence of low-signal regions, “spectral aliasing” (especially for long TE spacing, or at high field), and ambiguities and inaccuracies in the signal model (for instance, the signal model in Eq. [1] is ambiguous in voxels containing only water or only fat) (4, 8, 11–14).

A number of methods have been proposed for water/fat separation, which differ essentially in how they address the effects of field inhomogeneities in the acquired signal. Dixon's (9) original method assumes *f*_{B,q} = 0 and performs water/fat separation using only two images. Glover and Schneider (10) proposed a three-point method (*N* = 3) where the *t*_{n} are chosen such that *f*_{B,q} can be estimated directly from the first and third images, avoiding the nonlinearity of the problem. Xiang and An (15) proposed a method (termed “direct phase encoding”) that allows analytical separation of water and fat for a broader choice of *t*_{n} than the original three-point method. An and Xiang (16) introduced a method for fitting multiple spectral components using nonlinear least squares. Ma (17) introduced an improved two-point method where phase errors due to field inhomogeneities are corrected using a region-growing algorithm. Reeder et al. (4) introduced a novel method for iterative decomposition of water and fat with echo asymmetry and least squares estimation (IDEAL) where {*f*_{B,q}, ρ_{W,q} , ρ_{F,q}} are estimated independently at each voxel by an iterative nonlinear least squares fitting procedure. The IDEAL method has several desirable properties. For example, it works for arbitrary echo times and can result in the maximum-likelihood water/fat decomposition. However, the original IDEAL method has trouble dealing with large field inhomogeneities, due to the implicit assumption that the field inhomogeneity is moderate and the fact that only local convergence is guaranteed. Several extensions of IDEAL have been proposed in recent years to address the problem with large field inhomogeneities. Yu et al. (18) proposed a region-growing extension of IDEAL where field map smoothness is imposed by a region-growing process initialized with an automatically selected seed voxel. Tsao and Jiang (19) proposed a multiresolution method to help guide the selection of the correct decomposition at each voxel. Lu and Hargreaves (20) developed a method that combines region-growing and multiresolution by using region-growing at the coarsest resolution and propagating the resulting estimates to the finer resolutions.

This article reports a new method to estimate {*f*_{B,q}, ρ_{W,q}, ρ_{F,q}}, for *q* = 1,…,*Q*, jointly for all the voxels (in contrast to voxel-based estimation). Relative to a previous method presented in Hernando et al. (14) (and applied in Kellman et al. (3)), this article introduces: (i) a novel optimization method based on graph cuts, with improved theoretical properties and practical performance; (ii) a different weighting scheme for the cost function, designed to address problems with rapid field variations; and (iii) a novel and more detailed analysis of the spatial resolution properties of the estimated field map, as well as its effects on the resulting water/fat images. In the remainder of this paper, we will describe the proposed method and show some representative results from challenging cardiac imaging applications to demonstrate its performance.