Field Map Estimation Research Articles

Sampling strategies and integrated reconstruction for reducing distortion and boundary slice aliasing in high-resolution 3D diffusion MRI.

To develop a new method for high-fidelity, high-resolution 3D multi-slab diffusion MRI with minimal distortion and boundary slice aliasing. Our method modifies 3D multi-slab imaging to integrate blip-reversed acquisitions for distortion correction and oversampling in the slice direction (kz ) for reducing boundary slice aliasing. Our aim is to achieve robust acceleration to keep the scan time the same as conventional 3D multi-slab acquisitions, in which data are acquired with a single direction of blip traversal and without kz -oversampling. We employ a two-stage reconstruction. In the first stage, the blip-up/down images are respectively reconstructed and analyzed to produce a field map for each diffusion direction. In the second stage, the blip-reversed data and the field map are incorporated into a joint reconstruction to produce images that are corrected for distortion and boundary slice aliasing. We conducted experiments at 7T in six healthy subjects. Stage 1 reconstruction produces images from highly under-sampled data (R = 7.2) with sufficient quality to provide accurate field map estimation. Stage 2 joint reconstruction substantially reduces distortion artifacts with comparable quality to fully-sampled blip-reversed results (2.4× scan time). Whole-brain in-vivo results acquired at 1.22 mm and 1.05 mm isotropic resolutions demonstrate improved anatomical fidelity compared to conventional 3D multi-slab imaging. Data demonstrate good reliability and reproducibility of the proposed method over multiple subjects. The proposed acquisition and reconstruction framework provide major reductions in distortion and boundary slice aliasing for 3D multi-slab diffusion MRI without increasing the scan time, which can potentially produce high-quality, high-resolution diffusion MRI.

A field map updating algorithm to improve fat-water spiral imaging.

An accurate field map is essential to separate fat and water signals in a dual-echo chemical shift encoded spiral MRI scan. A rapid low-resolution B0 map prescan is usually performed before each exam. Occasional inaccuracy in these field map estimates can lead to misclassification of the water and fat signals as well as blurring artifacts in the reconstruction. The present work proposes a self-consistent model to evaluate residual field offsets according to the image data to improve the reconstruction quality and facilitate the scan efficiency. The proposed method compares the phase differences of the two-echo data after correcting for fat frequency offsets. A more accurate field map is approximated according to the phase discrepancies and improved image quality. Experiments were conducted with simulated off-resonance on a numerical phantom, five volunteer head scans, and four volunteer abdominal scans for validation. The initial reconstruction of the demonstrated examples exhibit blurring artifacts and misregistration of fat and water because of the inaccuracy of the field map. The proposed method updates the field map to amend the fat and water estimation and improve image quality. This work presents a model to improve the quality of fat-water imaging of the spiral MRI by estimating a better field map from the acquired data. It allows reducing the field map pre-scans before each spiral scan under normal circumstances to increase scan efficiency.

Robust breast quantitative susceptibility mapping in the presence of silicone.

To (a) develop a preconditioned water-fat-silicone total field inversion (wfsTFI) algorithm that directly estimates the susceptibility map from complex multi-echo data in the breast in the presence of silicone and to (b) evaluate the performance of wfsTFI for breast quantitative susceptibility mapping (QSM) in silico and in vivo in comparison with formerly proposed methods. Numerical simulations and in vivo multi-echo gradient echo breast measurements were performed to compare wfsTFI to a previously proposed field map-based linear total field inversion algorithm (lTFI) with and without the consideration of the chemical shift of silicone in the field map estimation step. Specifically, a simulation based on an in vivo scan and data from five patients were included in the analysis. In the simulation, wfsTFI is able to significantly decrease the normalized root mean square error from lTFI without (4.46) and with (1.77) the consideration of the chemical shift of silicone to 0.68. Both the in silico and in vivo wfsTFI susceptibility maps show reduced shadowing artifacts in local tissue adjacent to silicone, reduced streaking artifacts and no erroneous single voxels of diamagnetic susceptibility in proximity to silicone. The proposed wfsTFI method can automatically distinguish between subjects with and without silicone. Furthermore wfsTFI accounts for the presence of silicone in the QSM dipole inversion and allows for the robust estimation of susceptibility in proximity to silicone breast implants and hence allows the visualization of structures that would otherwise be dominated by artifacts on susceptibility maps.

On the water-fat in-phase assumption for quantitative susceptibility mapping.

To (a) define multi-peak fat model-based effective in-phase echo times for quantitative susceptibility mapping (QSM) in water-fat regions, (b) analyze the relationship between fat fraction, field map quantification bias and susceptibility bias, and (c) evaluate the susceptibility mapping performance of the proposed effective in-phase echoes in comparison to single-peak in-phase echoes and water-fat separation for regions where both water and fat are present. Effective multipeak in-phase echo times for a bone marrow and a liver fat spectral model were derived from a single voxel simulation. A Monte Carlo simulation was performed to assess the field map estimation error as a function of fat fraction for the different in-phase echoes. Additionally, a phantom scan and in vivo scans in the liver, spine, and breast were performed and evaluated with respect to quantification accuracy. The use of single-peak in-phase echoes can introduce a worst-case susceptibility bias of ppm. The use of effective multipeak in-phase echoes shows a similar quantitative performance in the numerical simulation, the phantom and in all in vivo anatomies when compared to water-fat separation-based QSM. QSM based on the proposed effective multipeak in-phase echoes can alleviate the quantification bias present in QSM based on single-peak in-phase echoes. When compared to water-fat separation-based QSM the proposed effective in-phase echo times achieve a similar quantitative performance while drastically reducing the computational expense for field map estimation.

Iterative static field map estimation for off‐resonance correction in non‐Cartesian susceptibility weighted imaging

Magnetic Resonance in MedicineVolume 88, Issue 5 p. C1-C1 COVER IMAGEFree Access Iterative static field map estimation for off-resonance correction in non-Cartesian susceptibility weighted imaging First published: 24 August 2022 https://doi.org/10.1002/mrm.29437AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume88, Issue5November 2022Pages C1-C1 RelatedInformation

Iterative static field map estimation for off‐resonance correction in non‐Cartesian susceptibility weighted imaging

Magnetic Resonance in MedicineVolume 88, Issue 4 p. C1-C1 COVER IMAGEFree Access Iterative static field map estimation for off-resonance correction in non-Cartesian susceptibility weighted imaging First published: 28 July 2022 https://doi.org/10.1002/mrm.29410AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume88, Issue4October 2022Pages C1-C1 RelatedInformation

Multisite reproducibility of quantitative susceptibility mapping and effective transverse relaxation rate in deep gray matter at 3 T using locally optimized sequences in 24 traveling heads

Iron concentration in the human brain plays a crucial role in several neurodegenerative diseases and can be monitored noninvasively using quantitative susceptibility mapping (QSM) and effective transverse relaxation rate (R2 *) mapping from multiecho T2 *-weighted images. Large population studies enable better understanding of pathologies and can benefit from pooling multisite data. However, reproducibility may be compromised between sites and studies using different hardware and sequence protocols. This work investigates QSM and R2 * reproducibility at 3T using locally optimized sequences from three centers and two vendors, and investigates possible reduction of cross-site variability through postprocessing approaches. Twenty-four healthy subjects traveled between three sites and were scanned twice at each site. Scan-rescan measurements from seven deep gray matter regions were used for assessing within-site and cross-site reproducibility using intraclass correlation coefficient (ICC) and within-subject standard deviation (SDw) measures. In addition, multiple QSM and R2 * postprocessing options were investigated with the aim to minimize cross-site sequence-related variations, including: mask generation approach, echo-timing selection, harmonizing spatial resolution, field map estimation, susceptibility inversion method, and linear field correction for magnitude images. The same-subject cross-site region of interest measurements for QSM and R2 * were highly correlated (R2 ≥ 0.94) and reproducible (mean ICC of 0.89 and 0.82 for QSM and R2 *, respectively). The mean cross-site SDw was 4.16 parts per billion (ppb) for QSM and 1.27 s-1 for R2 *. For within-site measurements of QSM and R2 *, the mean ICC was 0.97 and 0.87 and mean SDw was 2.36 ppb and 0.97 s-1 , respectively. The precision level is regionally dependent and is reduced in the frontal lobe, near brain edges, and in white matter regions. Cross-site QSM variability (mean SDw) was reduced up to 46% through postprocessing approaches, such as masking out less reliable regions, matching available echo timings and spatial resolution, avoiding the use of the nonconsistent magnitude contrast between scans in field estimation, and minimizing streaking artifacts.

Iterative static field map estimation for off-resonance correction in non-Cartesian susceptibility weighted imaging.

PurposePatient‐induced inhomogeneities in the magnetic field cause distortions and blurring during acquisitions with long readouts such as in susceptibility‐weighted imaging (SWI). Most correction methods require collecting an additional ΔB0 field map to remove these artifacts.TheoryThe static ΔB0 field map can be approximated with an acceptable error directly from a single echo acquisition in SWI. The main component of the observed phase is linearly related to ΔB0 and the echo time (TE), and the relative impact of non‐ ΔB0 terms becomes insignificant with TE >20 ms at 3 T for a well‐tuned system.MethodsThe main step is to combine and unfold the multi‐channel phase maps wrapped many times, and several competing algorithms are compared for this purpose. Four in vivo brain data sets collected using the recently proposed 3D spreading projection algorithm for rapid k‐space sampling (SPARKLING) readouts are used to assess the proposed method.ResultsThe estimated 3D field maps generated with a 0.6 mm isotropic spatial resolution provide overall similar off‐resonance corrections compared to reference corrections based on an external ΔB0 acquisitions, and even improved for 2 of 4 individuals. Although a small estimation error is expected, no aftermath was observed in the proposed corrections, whereas degradations were observed in the references.ConclusionA static ΔB0 field map estimation method was proposed to take advantage of acquisitions with long echo times, and outperformed the reference technique based on an external field map. The difference can be attributed to an inherent robustness to mismatches between volumes and external ΔB0 maps, and diverse other sources investigated.

Joint image and field map estimation for multi-echo hyperpolarized 13 C metabolic imaging of the heart.

Image reconstruction of metabolic images from hyperpolarized 13 C multi-echo data acquisition is sensitive to susceptibility-induced phase offsets, which are particularly challenging in the heart. A model-based framework for joint estimation of metabolite images and field map from echo shift-encoded data is proposed. Using simulations, it is demonstrated that correction of signal spilling due to incorrect decomposition of metabolites and geometrical distortions over a wide range of off-resonance gradients is possible. In vivo feasibility is illustrated using hyperpolarized [1-13 C]pyruvate in the pig heart. The model-based reconstruction for multi-echo, multicoil data was implemented as a nonconvex minimization problem jointly optimizing for metabolic images and B0 . A comprehensive simulation framework for echo shift-encoded hyperpolarized [1-13 C]pyruvate imaging was developed and applied to assess reconstruction performance and distortion correction of the proposed method. In vivo data were obtained in four pigs using hyperpolarized [1-13 C]pyruvate on a clinical 3T MR system with a six-channel receiver coil. Dynamic images were acquired during suspended ventilation using cardiac-triggered multi-echo single-shot echo-planar imaging in short-axis orientation. Simulations revealed that off-resonance gradients up to ±0.26ppm/pixel can be corrected for with reduced signal spilling and geometrical distortions yielding an accuracy of ≥90% in terms of Dice similarity index. In vivo, improved geometrical consistency (10% Dice improvement) compared to image reconstruction without field map correction and with reference to anatomical data was achieved. Joint image and field map estimation allows addressing off-resonance-induced geometrical distortions and metabolite spilling in hyperpolarized 13 C metabolic imaging of the heart.

Multi‐parametric artificial neural network fitting of phase‐cycled balanced steady‐state free precession data

Standard relaxation time quantification using phase-cycled balanced steady-state free precession (bSSFP), eg, motion-insensitive rapid configuration relaxometry (MIRACLE), is subject to a considerable underestimation of tissue T1 and T2 due to asymmetric intra-voxel frequency distributions. In this work, an artificial neural network (ANN) fitting approach is proposed to simultaneously extract accurate reference relaxation times (T1 , T2 ) and robust field map estimates ( , ΔB0 ) from the bSSFP profile. Whole-brain bSSFP data acquired at 3T were used for the training of a feedforward ANN with N = 12, 6, and 4 phase-cycles. The magnitude and phase of the Fourier transformed complex bSSFP frequency response served as input and the multi-parametric reference set [T1 , T2 , , ∆B0 ] as target. The ANN predicted relaxation times were validated against the target and MIRACLE. The ANN prediction of T1 and T2 for trained and untrained data agreed well with the reference, even for only four acquired phase-cycles. In contrast, relaxometry based on 4-point MIRACLE was prone to severe off-resonance-related artifacts. ANN predicted and ∆B0 maps showed the expected spatial inhomogeneity patterns in high agreement with the reference measurements for 12-point, 6-point, and 4-point bSSFP phase-cycling schemes. ANNs show promise to provide accurate brain tissue T1 and T2 values as well as reliable field map estimates. Moreover, the bSSFP acquisition can be accelerated by reducing the number of phase-cycles while still delivering robust T1 , T2 , , and ∆B0 estimates.

Efficient Regularized Field Map Estimation in 3D MRI.

Magnetic field inhomogeneity estimation is important in some types of magnetic resonance imaging (MRI), including field-corrected reconstruction for fast MRI with long readout times, and chemical shift based water-fat imaging. Regularized field map estimation methods that account for phase wrapping and noise involve nonconvex cost functions that require iterative algorithms. Most existing minimization techniques were computationally or memory intensive for 3D datasets, and are designed for single-coil MRI. This paper considers 3D MRI with optional consideration of coil sensitivity, and addresses the multi-echo field map estimation and water-fat imaging problem. Our efficient algorithm uses a preconditioned nonlinear conjugate gradient method based on an incomplete Cholesky factorization of the Hessian of the cost function, along with a monotonic line search. Numerical experiments show the computational advantage of the proposed algorithm over state-of-the-art methods with similar memory requirements.

Appropriate echo time selection for quantitative susceptibility mapping.

The purpose of our study was to clarify the dependence of quantitative susceptibility mapping (QSM) on echo time (TE). We constructed a phantom consisting of six tubes; three tubes were filled with different concentrations (0.5, 1.0, and 2.5mM) of gadopentetate dimeglumine (Gd-DTPA), and three were filled with different concentrations (100, 200, and 350mg/mL) of calcium hydroxyapatite. Real and imaginary images from multi-echo spoiled gradient-echo data (12 echoes) were acquired. We then used four datasets with three serial echoes. The QSM procedure consists of four steps: field map estimation, phase unwrapping, background removal, and dipole inversion. For each sample, we compared the measured mean susceptibility value with the theoretical susceptibility value and conducted a linear regression analysis. Accordingly, the relationship between the measured susceptibility and concentration of Gd-DTPA was shown to agree well with the theoretical values (TEs = 16.4, 20.8, and 25.2ms; slope = 0.24, R2 = 1.00). Furthermore, the relationship between the measured susceptibility and concentration of hydroxyapatite also showed good linearity (TEs = 16.4, 20.8, and 25.2ms; slope = - 0.00121, R2 = 1.00). In conclusion, the optimization of the TE in QSM makes it possible to obtain more detailed information regarding the susceptibility of biomaterials.

DRIFT-FREE INDOOR NAVIGATION USING SIMULTANEOUS LOCALIZATION AND MAPPING OF THE AMBIENT HETEROGENEOUS MAGNETIC FIELD

Abstract. In the absence of external reference position information (e.g. surveyed targets or Global Navigation Satellite Systems) Simultaneous Localization and Mapping (SLAM) has proven to be an effective method for indoor navigation. The positioning drift can be reduced with regular loop-closures and global relaxation as the backend, thus achieving a good balance between exploration and exploitation. Although vision-based systems like laser scanners are typically deployed for SLAM, these sensors are heavy, energy inefficient, and expensive, making them unattractive for wearables or smartphone applications. However, the concept of SLAM can be extended to non-optical systems such as magnetometers. Instead of matching features such as walls and furniture using some variation of the Iterative Closest Point algorithm, the local magnetic field can be matched to provide loop-closure and global trajectory updates in a Gaussian Process (GP) SLAM framework. With a MEMS-based inertial measurement unit providing a continuous trajectory, and the matching of locally distinct magnetic field maps, experimental results in this paper show that a drift-free navigation solution in an indoor environment with millimetre-level accuracy can be achieved. The GP-SLAM approach presented can be formulated as a maximum a posteriori estimation problem and it can naturally perform loop-detection, feature-to-feature distance minimization, global trajectory optimization, and magnetic field map estimation simultaneously. Spatially continuous features (i.e. smooth magnetic field signatures) are used instead of discrete feature correspondences (e.g. point-to-point) as in conventional vision-based SLAM. These position updates from the ambient magnetic field also provide enough information for calibrating the accelerometer bias and gyroscope bias in-use. The only restriction for this method is the need for magnetic disturbances (which is typically not an issue for indoor environments); however, no assumptions are required for the general motion of the sensor (e.g. static periods).

A Robust Method for Estimating B0 Inhomogeneity Field in the Liver by Mitigating Fat Signals and Phase-Wrapping.

We developed an optimized and robust method to estimate liver B0 field inhomogeneity for monitoring and correcting susceptibility-induced geometric distortion in magnetic resonance images for precision therapy. A triple-gradient-echo acquisition was optimized for the whole liver B0 field estimation within a single-exhale breath-hold scan on a 3 T scanner. To eliminate chemical-shift artifacts, fat signals were chosen in-phase between 2 echoes with an echo time difference (ΔTE) of 2.3 milliseconds. To avoid phase-wrapping, other 2 echoes provided a large field dynamic range (1/ΔTE) to cover the B0 field inhomogeneity. In addition, using high parallel imaging factor of 4 and a readout-bandwidth of 1955 Hz/pixel, an ∼18-second acquisition time for breath-held scans was achieved. A 2-step, 1-dimensional regularized method for the ΔB0 field map estimation was developed, tested and validated in phantom and patient studies. Our method was validated on a water phantom with fat components and air pockets; it yielded ΔB0-field maps that had no chemical-shift and phase-wrapping artifacts, and it had a <0.5 mm of geometric distortion near the air pockets. The ΔB0-field maps of the patients' abdominal regions were also free from phase-wrapping and chemical-shift artifacts. The maximum field inhomogeneity was found near the lung–liver interface, up to ∼300 Hz, resulting in ∼2 mm of distortions in anatomical images with a readout-bandwidth of 440 Hz/pixel. The field mapping method in the abdominal region is robust; it can be easily integrated in clinical workflow for patient-based quality control of magnetic resonance imaging geometric integrity.

Improved field-mapping and artifact correction in multispectral imaging.

To develop a method for improved B0 field-map estimation, deblurring, and image combination for multispectral imaging near metal. A goodness-of-fit field-map estimation technique is proposed that uses only the multispectral imaging (MSI) data to estimate the field map. Using the improved field map, a novel deblurring technique is proposed that also employs a new image combination scheme to reduce the effects of noise and other residual MSI artifacts. The proposed field-map estimation and deblurring techniques are compared to the current methods in phantoms and/or in vivo from subjects with knee, hip, and spinal metallic implants. Phantom experiments validate that the goodness-of-fit field-map estimation is less sensitive to noise and bias than the conventional center-of-mass technique, which reduces distortion in the deblurring methods. The new deblurring approach also is substantially less sensitive to noise and distortion than the current deblurring method, as demonstrated in phantoms and in vivo, and is able to find a good tradeoff between deblurring and distortion. The proposed methods not only enable field-mapping with reduced noise sensitivity but are able to create deblurred images with less distortion and better signal-to-noise ratio with no additional scan time, thereby enabling improved visualization of underlying anatomy near metallic implants. Magn Reson Med 78:2022-2034, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

A new gradient shimming method based on undistorted field map of B0 inhomogeneity

Most existing gradient shimming methods for NMR spectrometers estimate field maps that resolve B0 inhomogeneity spatially from dual gradient-echo (GRE) images acquired at different echo times. However, the distortions induced by B0 inhomogeneity that always exists in the GRE images can result in estimated field maps that are distorted in both geometry and intensity, leading to inaccurate shimming. This work proposes a new gradient shimming method based on undistorted field map of B0 inhomogeneity obtained by a more accurate field map estimation technique. Compared to the traditional field map estimation method, this new method exploits both the positive and negative polarities of the frequency encoded gradients to eliminate the distortions caused by B0 inhomogeneity in the field map. Next, the corresponding automatic post-data procedure is introduced to obtain undistorted B0 field map based on knowledge of the invariant characteristics of the B0 inhomogeneity and the variant polarity of the encoded gradient. The experimental results on both simulated and real gradient shimming tests demonstrate the high performance of this new method.

고자장 자기공명영상에서 효율적인 지방 정량화를 위한 필드 맵 측정 기술

고자장 자기공명영상에서 효율적인 지방 정량화를 위한 필드 맵 측정 기술

Simultaneous phase unwrapping and removal of chemical shift (SPURS) using graph cuts: application in quantitative susceptibility mapping.

Quantitative susceptibility mapping (QSM) is a magnetic resonance imaging technique that reveals tissue magnetic susceptibility. It relies on having a high quality field map, typically acquired with a relatively long echo spacing and long final TE. Applications of QSM outside the brain require the removal of fat contributions to the total signal phase. However, current water/fat separation methods applied on typical data acquired for QSM suffer from three issues: inadequacy when using large echo spacing, over-smoothing of the field maps and high computational cost. In this paper, the general phase wrap and chemical shift problem is formulated using a single species fitting and is solved using graph cuts with conditional jump moves. This method is referred as simultaneous phase unwrapping and removal of chemical shift (SPURS). The result from SPURS is then used as the initial guess for a voxel-wise iterative decomposition of water and fat with echo asymmetric and least-squares estimation (IDEAL). The estimated 3-D field maps are used to compute QSM in body regions outside of the brain, such as the liver. Experimental results show substantial improvements in field map estimation, water/fat separation and reconstructed QSM compared to two existing water/fat separation methods on 1.5T and 3T magnetic resonance human data with long echo spacing and rapid field map variation.

Estimation of geometrically undistorted B0 inhomogeneity maps

Geometric accuracy of MRI is one of the main concerns for its use as a sole image modality in precision radiation therapy (RT) planning. In a state-of-the-art scanner, system level geometric distortions are within acceptable levels for precision RT. However, subject-induced B0 inhomogeneity may vary substantially, especially in air-tissue interfaces. Recent studies have shown distortion levels of more than 2 mm near the sinus and ear canal are possible due to subject-induced field inhomogeneity. These distortions can be corrected with the use of accurate B0 inhomogeneity field maps. Most existing methods estimate these field maps from dual gradient-echo (GRE) images acquired at two different echo-times under the assumption that the GRE images are practically undistorted. However distortion that may exist in the GRE images can result in estimated field maps that are distorted in both geometry and intensity, leading to inaccurate correction of clinical images. This work proposes a method for estimating undistorted field maps from GRE acquisitions using an iterative joint estimation technique. The proposed method yields geometrically corrected GRE images and undistorted field maps that can also be used for the correction of images acquired by other sequences. The proposed method is validated through simulation, phantom experiments and applied to patient data. Our simulation results show that our method reduces the root-mean-squared error of the estimated field map from the ground truth by ten-fold compared to the distorted field map. Both the geometric distortion and the intensity corruption (artifact) in the images caused by the B0 field inhomogeneity are corrected almost completely. Our phantom experiment showed improvement in the geometric correction of approximately 1 mm at an air-water interface using the undistorted field map compared to using a distorted field map. The proposed method for undistorted field map estimation can lead to improved geometric distortion correction at air-tissue interfaces, especially in low readout-bandwidth acquisitions, thus making them suitable for clinical use in precision RT without increasing the treatment planning margin.

Fat water decomposition using globally optimal surface estimation (GOOSE) algorithm

This article focuses on developing a novel noniterative fat water decomposition algorithm more robust to fat water swaps and related ambiguities. Field map estimation is reformulated as a constrained surface estimation problem to exploit the spatial smoothness of the field, thus minimizing the ambiguities in the recovery. Specifically, the differences in the field map-induced frequency shift between adjacent voxels are constrained to be in a finite range. The discretization of the above problem yields a graph optimization scheme, where each node of the graph is only connected with few other nodes. Thanks to the low graph connectivity, the problem is solved efficiently using a noniterative graph cut algorithm. The global minimum of the constrained optimization problem is guaranteed. The performance of the algorithm is compared with that of state-of-the-art schemes. Quantitative comparisons are also made against reference data. The proposed algorithm is observed to yield more robust fat water estimates with fewer fat water swaps and better quantitative results than other state-of-the-art algorithms in a range of challenging applications. The proposed algorithm is capable of considerably reducing the swaps in challenging fat water decomposition problems. The experiments demonstrate the benefit of using explicit smoothness constraints in field map estimation and solving the problem using a globally convergent graph-cut optimization algorithm.