Reconstruction of MRI data encoded with arbitrarily shaped,curvilinear, nonbijective magnetic fields

A basic framework for image reconstruction from spatial encoding by curvilinear, nonbijective magnetic encoding fields in combination with multiple receivers is presented. The theory was developed in the context of the recently introduced parallel imaging technique using localized gradients (PatLoc) approach. In this new imaging modality, the linear gradient fields are generalized to arbitrarily shaped, nonbijective spatial encoding magnetic fields, which lead to ambiguous encoding. Ambiguities are resolved by adaptation of concepts developed for parallel imaging. Based on theoretical considerations, a practical algorithm for Cartesian trajectories is derived in the case that the conventional gradient coils are replaced by coils for PatLoc. The reconstruction method extends Cartesian sensitivity encoding (SENSE) reconstruction with an additional voxelwise intensity‐correction step. Spatially varying resolution, signal‐to‐noise ratio, and truncation artifacts are described and analyzed. Theoretical considerations are validated by two‐dimensional simulations based on multipolar encoding fields and they are confirmed by applying the reconstruction algorithm to initial experimental data. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Respiratory and cardiac self‐gated free‐breathing cardiac CINE imaging with multiecho 3D hybrid radial SSFP acquisition

A respiratory and cardiac self‐gated free‐breathing three‐dimensional cine steady‐state free precession imaging method using multiecho hybrid radial sampling is presented. Cartesian mapping of the k‐space center along the slice encoding direction provides intensity‐weighted position information, from which both respiratory and cardiac motions are derived. With in plan radial sampling acquired at every pulse repetition time, no extra scan time is required for sampling the k‐space center. Temporal filtering based on density compensation is used for radial reconstruction to achieve high signal‐to‐noise ratio and contrast‐to‐noise ratio. High correlation between the self‐gating signals and external gating signals is demonstrated. This respiratory and cardiac self‐gated, free‐breathing, three‐dimensional, radial cardiac cine imaging technique provides image quality comparable to that acquired with the multiple breath‐hold two‐dimensional Cartesian steady‐state free precession technique in short‐axis, four‐chamber, and two‐chamber orientations. Functional measurements from the three‐dimensional cardiac short axis cine images are found to be comparable to those obtained using the standard two‐dimensional technique. Magn Reson Med 63:1230–1237, 2010. © 2010 Wiley‐Liss, Inc.     

Continuously moving table time‐of‐flight angiography of the peripheral veins

Time‐of‐flight (TOF) MR angiography allows for noninvasive vessel imaging. To overcome the limited volumetric coverage of standard TOF techniques, the aim of this study was to investigate the combination of TOF and continuously moving table (CMT) acquisitions for peripheral vein imaging based on image subtraction. Two acquisition strategies are presented: a simple two‐step method based on 2‐fold CMT acquisition and an advanced one‐step method requiring only one continuous scan. Image quality of both CMT TOF techniques was evaluated by semiquantitative image grading and by signal‐to‐noise ratio and contrast‐to‐noise ratio analysis for veins of the upper and lower leg in 10 healthy volunteers. Results were compared to a standard stationary two‐dimensional (2D) TOF multistation acquisition. Image grading revealed good image quality for both CMT TOF methods, thereby confirming the feasibility of axial 2D CMT TOF to assess the veins of the lower extremities during a single scan. Quantitative evaluation showed no significant difference in signal‐to‐noise ratio and contrast‐to‐noise ratio compared to the stationary experiment. Additional measurements in three patients with postthrombotic changes and varicosities demonstrated the clinical applicability of the presented methods. CMT TOF provides promising results and permits the detection of various pathologic changes of the venous system. Magn Reson Med 63:1219–1229, 2010. © 2010 Wiley‐Liss, Inc.     

Independent slab‐phase modulation combined with parallel imaging in bilateral breast MRI

Independent slab‐phase modulation allows three‐dimensional imaging of multiple volumes without encoding the space between volumes, thus reducing scan time. Parallel imaging further accelerates data acquisition by exploiting coil sensitivity differences between volumes. This work compared bilateral breast image quality from self‐calibrated parallel imaging reconstruction methods such as modified sensitivity encoding, generalized autocalibrating partially parallel acquisitions and autocalibrated reconstruction for Cartesian sampling (ARC) for data with and without slab‐phase modulation. A study showed an improvement of image quality by incorporating slab‐phase modulation. Geometry factors measured from phantom images were more homogenous and lower on average when slab‐phase modulation was used for both mSENSE and GRAPPA reconstructions. The resulting improved signal‐to‐noise ratio (SNR) was validated for in vivo images as well using ARC instead of GRAPPA, illustrating average SNR efficiency increases in mSENSE by 5% and ARC by 8% based on region of interest analysis. Furthermore, aliasing artifacts from mSENSE reconstruction were reduced when slab‐phase modulation was used. Overall, slab‐phase modulation with parallel imaging improved image quality and efficiency for 3D bilateral breast imaging. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Comparative SNR for high‐throughput mouse embryo MR microscopy

MR microscopy is being explored as a useful imaging tool to phenotype mouse embryos due to its volume coverage with three‐dimensional isotropic resolution. However, the main limitation for mouse embryo MR microscopy is the signal‐to‐noise ratio. Large numbers of embryos are needed for phenotypic screening, making high throughput essential. Two high‐throughput imaging approaches, multi‐embryo shared‐coil (shared) and multi‐embryo individual‐coil (individual), have been developed for phenotyping mouse embryos. This study quantitatively compares the signal‐to‐noise ratio at equivalent times between these two established methods by compensating for differences that result from field strength. While the individual method provides 3.3 times as much signal‐to‐noise ratio as the shared method at equivalent conditions, it is more difficult and expensive to implement. Furthermore, the number of embryos that can be imaged concurrently is limited by the number of receiver channels. The objective of this study is to provide measured comparative data to guide choices for high‐throughput mouse embryo MR microscopy and other similar applications. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Rapid MR‐ARFI method for focal spot localization during focused ultrasound therapy

MR‐guided focused ultrasound (FUS) is a noninvasive therapy for treating various pathologies. MR‐based acoustic radiation force imaging (MR‐ARFI) measures tissue displacement in the focal spot due to acoustic radiation force. MR‐ARFI also provides feedback for adaptive focusing algorithms that could correct for phase aberrations caused by the skull during brain treatments. This work developed a single‐shot echo‐planar imaging–based MR‐ARFI method that reduces scan time and ultrasound energy deposition. The new method was implemented and tested in a phantom and ex vivo brain tissue. The effect of the phase aberrations on the ultrasound focusing was studied using displacement maps obtained with echo‐planar imaging and two‐dimensional spin‐warp MR‐ARFI. The results show that displacement in the focal spot can be rapidly imaged using echo‐planar imaging–based MR‐ARFI with high signal‐to‐noise ratio efficiency and without any measurable tissue heating. Echo‐planar imaging–based displacement images also demonstrate sufficient sensitivity to phase aberrations and can serve as rapid feedback for adaptive focusing in brain treatments and other applications. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.     

Adapting MRI acoustic radiation force imaging for in vivo human brain focused ultrasound applications

A variety of magnetic resonance imaging acoustic radiation force imaging (MR‐ARFI) pulse sequences as the means for image guidance of focused ultrasound therapy have been recently developed and tested ex vivo and in animal models. To successfully translate MR‐ARFI guidance into human applications, ensuring that MR‐ARFI provides satisfactory image quality in the presence of patient motion and deposits safe amount of ultrasound energy during image acquisition is necessary. The first aim of this work was to study the effect of motion on in vivo displacement images of the brain obtained with 2D Fourier transform spin echo MR‐ARFI. Repeated bipolar displacement encoding configuration was shown less sensitive to organ motion. The optimal signal‐to‐noise ratio of displacement images was found for the duration of encoding gradients of 12 ms. The second aim was to further optimize the displacement signal‐to‐noise ratio for a particular tissue type by setting the time offset between the ultrasound emission and encoding based on the tissue response to acoustic radiation force. A method for measuring tissue response noninvasively was demonstrated. Finally, a new method for simultaneous monitoring of tissue heating during MR‐ARFI acquisition was presented to enable timely adjustment of the ultrasound energy aimed at ensuring the safety of the MR‐ARFI acquisition. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.     

Optimization of encoding gradients for MR‐ARFI

MR acoustic radiation force imaging provides a promising method to monitor therapeutic ultrasound treatments. By measuring the displacement induced by the acoustic radiation force, MR acoustic radiation force imaging can locate the focal spot, without a significant temperature rise. In this work, the encoding gradient for MR acoustic radiation force imaging is optimized to achieve an enhanced accuracy and precision of the displacement measurement. By analyzing the sources of artifacts, bulk motion and eddy currents are shown to introduce errors to the measurement, and heavy diffusion‐weighting is shown to result in noisy displacement maps. To eliminate these problems, a new encoding scheme is proposed, which utilizes a pair of bipolar gradients. Improved precision is achieved with robustness against bulk motion and background phase distortion, and improved accuracy is achieved with reduced diffusion‐weighting and optimized encoding pulse width. The experiment result shows that the signal‐to‐noise ratio can be enhanced by more than 2‐fold. These significant improvements are obtained at no cost of scan time or encoding sensitivity, enabling the detection of a displacement less than 0.l μm in a gel phantom with MR acoustic radiation force imaging. Magn Reson Med 63:1050–1058, 2010. © 2010 Wiley‐Liss, Inc.     

4D phase contrast MRI at 3 T: Effect of standard and blood‐pool contrast agents on SNR,PC‐MRA,and blood flow visualization

Time‐resolved phase contrast (PC) MRI with velocity encoding in three directions (flow‐sensitive four‐dimensional MRI) can be employed to assess three‐dimensional blood flow in the entire aortic lumen within a single measurement. These data can be used not only for the visualization of blood flow but also to derive additional information on vascular geometry with three‐dimensional PC MR angiography (MRA). As PC‐MRA is sensitive to available signal‐to‐noise ratio, standard and novel blood pool contrast agents may help to enhance PC‐MRA image quality. In a group of 30 healthy volunteers, the influence of different contrast agents on vascular signal‐to‐noise ratio, PC‐MRA quality, and subsequent three‐dimensional stream‐line visualization in the thoracic aorta was determined. Flow‐sensitive four‐dimensional MRI data acquired with contrast agent provided significantly improved signal‐to‐noise ratio in magnitude data and noise reduction in velocity data compared to measurements without contrast media. The agreement of three‐dimensional PC‐MRA with reference standard contrast‐enhanced MRA was good for both contrast agents, with improved PC‐MRA performance for blood pool contrast agent, particularly for the smaller supra‐aortic branches. For three‐dimensional flow visualization, a trend toward improved results for the data with contrast agent was observed. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

SENSE with improved tolerance to inaccuracies in coil sensitivity maps

In this work, an extension of the Cartesian sensitivity encoding (SENSE) parallel imaging framework is proposed. In the well‐known SENSE solution, the overdetermined reconstruction inversion problem is optimized to get the highest signal‐to‐noise ratio in the image. In this extension, the probability of artifacts due to incorrect knowledge of the receiver coil sensitivities is also taken into account. This is realized by assuming an uncertainty in measured receiver coil sensitivities to enable weighting of residual artifact level and signal‐to‐noise ratio in the inversion problem. This inversion problem can still be solved by a least‐squares optimization without the need of any complex iterative scheme. Results in abdominal imaging show that artifact levels can be substantially reduced, at the cost of a signal‐to‐noise ratio penalty. The size of the signal‐to‐noise ratio penalty depends on the assumed inaccuracy of the coil sensitivities, sensitivity encoding acceleration factor, and coil configuration. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.     

A 2D MTF approach to evaluate and guide dynamic imaging developments

As the number and complexity of partially sampled dynamic imaging methods continue to increase, reliable strategies to evaluate performance may prove most useful. In the present work, an analytical framework to evaluate given reconstruction methods is presented. A perturbation algorithm allows the proposed evaluation scheme to perform robustly without requiring knowledge about the inner workings of the method being evaluated. A main output of the evaluation process consists of a two‐dimensional modulation transfer function, an easy‐to‐interpret visual rendering of a method's ability to capture all combinations of spatial and temporal frequencies. Approaches to evaluate noise properties and artifact content at all spatial and temporal frequencies are also proposed. One fully sampled phantom and three fully sampled cardiac cine datasets were subsampled (R = 4 and 8) and reconstructed with the different methods tested here. A hybrid method, which combines the main advantageous features observed in our assessments, was proposed and tested in a cardiac cine application, with acceleration factors of 3.5 and 6.3 (skip factors of 4 and 8, respectively). This approach combines features from methods such as k‐t sensitivity encoding, unaliasing by Fourier encoding the overlaps in the temporal dimension‐sensitivity encoding, generalized autocalibrating partially parallel acquisition, sensitivity profiles from an array of coils for encoding and reconstruction in parallel, self, hybrid referencing with unaliasing by Fourier encoding the overlaps in the temporal dimension and generalized autocalibrating partially parallel acquisition, and generalized autocalibrating partially parallel acquisition–enhanced sensitivity maps for sensitivity encoding reconstructions. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

Assessment of MR compatibility of a PET insert developed for simultaneous multiparametric PET/MR imaging on an animal system operating at 7 T

The combination of positron emission tomography and MR in one system is currently emerging and opens up new domains in the functional examinations of living systems. This article reports on relevant influences of a positron emission tomography insert on MR imaging. The basic conditions of main magnetic field and RF field homogeneity were measured as well as image quality and signal‐to‐noise ratio when applying the usual MR sequence types including echo‐planar techniques. Moreover, the influence of the positron emission tomography insert on the RF noise level and on RF interferences was measured by comparing results achieved with and without the positron emission tomography insert. The temporal stability of EPI imaging with and without the positron emission tomography insert was assessed. Small but significant decreases in the signal‐to‐noise ratio were revealed when the positron emission tomography insert was present, whereas B₀ and B₁ homogeneity as well as RF noise level were not adversely affected. A higher signal intensity drift was found for EPI imaging studies; however, this can be compensated by post processing. In summary, this study shows that positron emission tomography inserts can be designed for and used within an MR system practically, without substantially affecting the MR image quality. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Robust GRAPPA reconstruction and its evaluation with the perceptual difference model

PURPOSE: To develop and optimize a new modification of GRAPPA (generalized autocalibrating partially parallel acquisitions) MR reconstruction algorithm named "Robust GRAPPA." MATERIALS AND METHODS: In Robust GRAPPA, k-space data points were weighted before the reconstruction. Small or zero weights were assigned to "outliers" in k-space. We implemented a Slow Robust GRAPPA method, which iteratively reweighted the k-space data. It was compared to an ad hoc Fast Robust GRAPPA method, which eliminated (assigned zero weights to) a fixed percentage of k-space "outliers" following an initial estimation procedure. In comprehensive experiments the new algorithms were evaluated using the perceptual difference model (PDM), whereby image quality was quantitatively compared to the reference image. Independent variables included algorithm type, total reduction factor, outlier ratio, center filling options, and noise across multiple image datasets, providing 10,800 test images for evaluation. RESULTS: The Fast Robust GRAPPA method gave results very similar to Slow Robust GRAPPA, and showed significant improvements as compared to regular GRAPPA. Fast Robust GRAPPA added little computation time compared with regular GRAPPA. CONCLUSION: Robust GRAPPA was proposed and proved useful for improving the reconstructed image quality. PDM was helpful in designing and optimizing the MR reconstruction algorithms.     

Spiral water-fat imaging with integrated off-resonance correction on a clinical scanner

Purpose

To integrate water‐fat–resolved spiral gradient‐echo imaging with off‐resonance correction into a clinical MR scanner and to evaluate its basic feasibility and performance.

Materials and Methods

Three‐point chemical shift imaging was implemented with forward and strongly T₂*‐weighted reverse spiral sampling and with off‐resonance correction after water–fat separation. It was applied in a volunteer study on single breathhold abdominal imaging, which included a brief comparison with Cartesian sampling.

Results

Water‐fat–resolved, off‐resonance–corrected forward and reverse three‐dimensional interleaved spiral imaging was found to be feasible on a clinical MR scanner with only minor changes to the existing data acquisition and reconstruction, and to provide good image quality. Three‐point chemical shift encoded data thus support both, water–fat separation and off‐resonance correction with high accuracy.

Conclusion

The combination of chemical shift encoding and appropriate postprocessing could pave the way for water‐fat–resolved spiral imaging in clinical applications. J. Magn. Reson. Imaging 2010;32:1262–1267. © 2010 Wiley‐Liss, Inc.     

Echo‐planar spectroscopic imaging (EPSI) of the water resonance structure in human breast using sensitivity encoding (SENSE)

High spectral and spatial resolution MRI, based on echo‐planar spectroscopic imaging, has been applied successfully in diagnostic breast imaging, but acquisition times are long. One way of increasing acquisition speed is to apply the sensitivity encoding algorithm for complex high spectral and spatial resolution data. We demonstrate application of a complex sensitivity encoding algorithm to high spectral and spatial resolution MRI data, in a phantom and human breast, with 7‐ and 16‐channel dedicated breast phased‐array coils. Very low g factors are obtained using the breast coils, and the signal‐to‐noise ratio (SNR) penalty for water resonance peak height and water resonance asymmetry images is small at acceleration factors of up to 6 and 4, respectively, as evidenced by high Pearson correlation factors between fully sampled and accelerated data. This is the first application of the sensitivity encoding algorithm to characterize the structure of the water resonance at high spatial resolution. Magn Reson Med 63:1557–1563, 2010. © 2010 Wiley‐Liss, Inc.     

Statistical noise analysis in GRAPPA using a parametrized noncentral Chi approximation model

The characterization of the distribution of noise in the magnitude MR image is a very important problem within image processing algorithms. The Rician noise assumed in single‐coil acquisitions has been the keystone for signal‐to‐noise ratio estimation, image filtering, or diffusion tensor estimation for years. With the advent of parallel protocols such as sensitivity encoding or Generalized Autocalibrated Partially Parallel Acquisitions that allow accelerated acquisitions, this noise model no longer holds. Since Generalized Autocalibrated Partially Parallel Acquisitions reconstructions yield the combination of the squared signals recovered at each receiving coil, noncentral Chi statistics have been previously proposed to model the distribution of noise. However, we prove in this article that this is a weak model due to several artifacts in the acquisition scheme, mainly the correlation existing between the signals obtained at each coil. Alternatively, we propose to model such correlations with a reduction in the number of degrees of freedom of the signal, which translates in an equivalent nonaccelerated system with a minor number of independent receiving coils and, consequently, a lower signal‐to‐noise ratio. With this model, a noncentral Chi distribution can be assumed for all pixels in the image, whose effective number of coils and effective variance of noise can be explicitly computed in a closed form from the Generalized Autocalibrated Partially Parallel Acquisitions interpolation coefficients. Extensive experiments over both synthetic and in vivo data sets have been performed to show the goodness of fit of out model. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Phase‐field dithering for active catheter tracking

A strategy to increase the robustness of active MR tracking of microcoils in low signal‐to‐noise ratio conditions was developed and tested. The method employs dephasing magnetic field gradient pulses that are applied orthogonal to the frequency‐encoding gradient pulse used in conventional point‐source MR tracking. In subsequent acquisitions, the orthogonal dephasing gradient pulse is rotated while maintaining a perpendicular orientation with respect to the frequency‐encoding gradient. The effect of the dephasing gradient is to apply a spatially dependent phase shift in directions perpendicular to the frequency‐encoding gradient. Since the desired MR signal for robust MR tracking comes from the small volume of nuclear spins near the small detection coil, the desired signal is not dramatically altered by the dephasing gradient. Undesired MR signals arising from larger volumes (e.g., due to coupling with the body coil or surface coils), on the other hand, are dephased and reduced in signal intensity. Since the approach requires no a priori knowledge of the microcoil orientation with respect to the main magnetic field, data from several orthogonal dephasing gradients are acquired and analyzed in real time. One of several selection algorithms is employed to identify the “best” data for use in the coil localization algorithm. This approach was tested in flow phantoms and animal models, with several multiplexing schemes, including the Hadamard and zero‐phase reference approaches. It was found to provide improved MR tracking of untuned microcoils. It also dramatically improved MR tracking robustness in low signal‐to‐noise‐ratio conditions and permitted tracking of microcoils that were inductively coupled to the body coil. Magn Reson Med 63:1398–1403, 2010. © 2010 Wiley‐Liss, Inc.     

3D magnetization‐prepared imaging using a stack‐of‐rings trajectory

Efficient acquisition strategies for magnetization‐prepared imaging based on the three‐dimensional (3D) stack‐of‐rings k‐space trajectory are presented in this work. The 3D stack‐of‐rings can be acquired with centric ordering in all three dimensions for greater efficiency in capturing the desired contrast. In addition, the 3D stack‐of‐rings naturally supports spherical coverage in k‐space for shorter scan times while achieving isotropic spatial resolution. While non‐Cartesian trajectories generally suffer from greater sensitivity to system imperfections, the 3D stack‐of‐rings can enhance magnetization‐prepared imaging with a high degree of robustness to timing delays and off‐resonance effects. As demonstrated with phantom scans, timing errors and gradient delays only cause a bulk rotation of the 3D stack‐of‐rings reconstruction. Furthermore, each ring can be acquired with a time‐efficient retracing design to resolve field inhomogeneities and enable fat/water separation. To demonstrate its effectiveness, the 3D stack‐of‐rings are considered for the case of inversion‐recovery‐prepared structural brain imaging. Experimental results show that the 3D stack‐of‐rings can achieve higher signal‐to‐noise ratio and higher contrast‐to‐noise ratio within a shorter scan time when compared to the standard inversion‐recovery‐prepared sequence based on 3D Cartesian encoding. The design principles used for this specific case of inversion‐recovery‐prepared brain imaging can be applied to other magnetization‐prepared imaging applications. Magn Reson Med 63:1210–1218, 2010. © 2010 Wiley‐Liss, Inc.     

Practical signal-to-noise ratio quantification for sensitivity encoding: application to coronary MR angiography

Purpose:

To develop and evaluate a practical method for the quantification of signal‐to‐noise ratio (SNR) on coronary MR angiograms (MRA) acquired with parallel imaging.

Materials and Methods:

To quantify the spatially varying noise due to parallel imaging reconstruction, a new method has been implemented incorporating image data acquisition followed by a fast noise scan during which radiofrequency pulses, cardiac triggering and navigator gating are disabled. The performance of this method was evaluated in a phantom study where SNR measurements were compared with those of a reference standard (multiple repetitions). Subsequently, SNR of myocardium and posterior skeletal muscle was determined on in vivo human coronary MRA.

Results:

In a phantom, the SNR measured using the proposed method deviated less than 10.1% from the reference method for small geometry factors (≤2). In vivo, the noise scan for a 10 min coronary MRA acquisition was acquired in 30 s. Higher signal and lower SNR, due to spatially varying noise, were found in myocardium compared with posterior skeletal muscle.

Conclusion:

SNR quantification based on a fast noise scan is a validated and easy‐to‐use method when applied to three‐dimensional coronary MRA obtained with parallel imaging as long as the geometry factor remains low. J. Magn. Reson. Imaging 2011;33:1330–1340. © 2011 Wiley‐Liss, Inc.     

Comprehensive quantification of signal‐to‐noise ratio and g‐factor for image‐based and k‐space‐based parallel imaging reconstructions

Parallel imaging reconstructions result in spatially varying noise amplification characterized by the g‐factor, precluding conventional measurements of noise from the final image. A simple Monte Carlo based method is proposed for all linear image reconstruction algorithms, which allows measurement of signal‐to‐noise ratio and g‐factor and is demonstrated for SENSE and GRAPPA reconstructions for accelerated acquisitions that have not previously been amenable to such assessment. Only a simple “prescan” measurement of noise amplitude and correlation in the phased‐array receiver, and a single accelerated image acquisition are required, allowing robust assessment of signal‐to‐noise ratio and g‐factor. The “pseudo multiple replica” method has been rigorously validated in phantoms and in vivo, showing excellent agreement with true multiple replica and analytical methods. This method is universally applicable to the parallel imaging reconstruction techniques used in clinical applications and will allow pixel‐by‐pixel image noise measurements for all parallel imaging strategies, allowing quantitative comparison between arbitrary k‐space trajectories, image reconstruction, or noise conditioning techniques. Magn Reson Med 60:895–907, 2008. © 2008 Wiley‐Liss, Inc.