Iterative image reconstruction for PROPELLER‐MRI using the nonuniform fast fourier transform

Purpose:

To investigate an iterative image reconstruction algorithm using the nonuniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) MRI.

Materials and Methods:

Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it with that of conventional gridding. The trade‐off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated.

Results:

It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased signal to noise ratio, reduced artifacts, for similar spatial resolution, compared with gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER‐MRI was maintained when using the iterative reconstruction approach.

Conclusion:

An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter, the new reconstruction technique may provide PROPELLER images with improved image quality compared with conventional gridding. J. Magn. Reson. Imaging 2010;32:211–217. © 2010 Wiley‐Liss, Inc.     

Motion correction in periodically‐rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) and turboprop MRI

Periodically‐rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) and Turboprop MRI are characterized by greatly reduced sensitivity to motion, compared to their predecessors, fast spin‐echo (FSE) and gradient and spin‐echo (GRASE), respectively. This is due to the inherent self‐navigation and motion correction of PROPELLER‐based techniques. However, it is unknown how various acquisition parameters that determine k‐space sampling affect the accuracy of motion correction in PROPELLER and Turboprop MRI. The goal of this work was to evaluate the accuracy of motion correction in both techniques, to identify an optimal rotation correction approach, and determine acquisition strategies for optimal motion correction. It was demonstrated that blades with multiple lines allow more accurate estimation of motion than blades with fewer lines. Also, it was shown that Turboprop MRI is less sensitive to motion than PROPELLER. Furthermore, it was demonstrated that the number of blades does not significantly affect motion correction. Finally, clinically appropriate acquisition strategies that optimize motion correction are discussed for PROPELLER and Turboprop MRI. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

3D diffusion tensor MRI with isotropic resolution using a steady‐state radial acquisition

Purpose

To obtain diffusion tensor images (DTI) over a large image volume rapidly with 3D isotropic spatial resolution, minimal spatial distortions, and reduced motion artifacts, a diffusion‐weighted steady‐state 3D projection (SS 3DPR) pulse sequence was developed.

Materials and Methods

A diffusion gradient was inserted in a SS 3DPR pulse sequence. The acquisition was synchronized to the cardiac cycle, linear phase errors were corrected along the readout direction, and each projection was weighted by measures of consistency with other data. A new iterative parallel imaging reconstruction method was also implemented for removing off‐resonance and undersampling artifacts simultaneously.

Results

The contrast and appearance of both the fractional anisotropy and eigenvector color maps were substantially improved after all correction techniques were applied. True 3D DTI datasets were obtained in vivo over the whole brain (240 mm field of view in all directions) with 1.87 mm isotropic spatial resolution, six diffusion encoding directions in under 19 minutes.

Conclusion

A true 3D DTI pulse sequence with high isotropic spatial resolution was developed for whole brain imaging in under 20 minutes. To minimize the effects of brain motion, a cardiac synchronized, multiecho, DW‐SSFP pulse sequence was implemented. Motion artifacts were further reduced by a combination of linear phase correction, corrupt projection detection and rejection, sampling density reweighting, and parallel imaging reconstruction. The combination of these methods greatly improved the quality of 3D DTI in the brain. J. Magn. Reson. Imaging 2009;29:1175–1184. © 2009 Wiley‐Liss, Inc.     

DC‐gated high resolution three‐dimensional lung imaging during free‐breathing

Purpose:

To use the acquisition of the k‐space center signal (DC signal) implemented into a Cartesian three‐dimensional (3D) FLASH sequence for retrospective respiratory self‐gating and, thus, for the examination of the whole human lung in high spatial resolution during free breathing.

Materials and Methods:

Volunteer as well as patient measurements were performed under free breathing conditions. The DC signal is acquired after the actual image data acquisition within each excitation of a 3D FLASH sequence. The DC signal is then used to track respiratory motion for retrospective respiratory gating.

Results:

It is shown that the acquisition of the DC signal after the imaging module can be used in a 3D FLASH sequence to extract respiratory motion information for retrospective respiratory self‐gating and allows for shorter echo times (TE) and therefore increased lung parenchyma SNR.

Conclusion:

The acquisition of the DC signal after image signal acquisition allows successful retrospective gating, enabling the reconstruction of high resolution images of the whole human lung under free breathing conditions. J. Magn. Reson. Imaging 2013;37:727–732. © 2012 Wiley Periodicals, Inc.     

Regularized iterative reconstruction for undersampled BLADE and its applications in three‐point Dixon water–fat separation

In MRI, the suppression of fat signal is very important for many applications. Multipoint Dixon based water–fat separation methods are commonly used due to its robustness to B₀ homogeneity compared with other fat suppression methods, such as spectral fat saturation. The traditional Cartesian k‐space trajectory based multipoint Dixon technique is sensitive to motion, such as pulsatile blood flow, resulting in artifacts that compromise image quality. This work presents a three‐point Dixon water–fat separation method using undersampled BLADE (aka PROPELLER) for motion robustness and speed. A regularized iterative reconstruction method is then proposed for reducing the streaking artifacts coming from undersampling. In this study, the performance of the regularized iterative reconstruction method is first tested by simulations and on MR phantoms. The performance of the proposed technique is then evaluated in vivo by comparing it with conventional fat suppression methods on the human brain and knee. Experiments show that the presented method delivers reliable water–fat separation results. The reconstruction method suppresses streaking artifacts typical for undersampled BLADE acquisition schemes without missing fine structures in the image. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Diffusion tensor imaging (DTI) with retrospective motion correction for large-scale pediatric imaging

Purpose:

To develop and implement a clinical DTI technique suitable for the pediatric setting that retrospectively corrects for large motion without the need for rescanning and/or reacquisition strategies, and to deliver high‐quality DTI images (both in the presence and absence of large motion) using procedures that reduce image noise and artifacts.

Materials and Methods:

We implemented an in‐house built generalized autocalibrating partially parallel acquisitions (GRAPPA)‐accelerated diffusion tensor (DT) echo‐planar imaging (EPI) sequence at 1.5T and 3T on 1600 patients between 1 month and 18 years old. To reconstruct the data, we developed a fully automated tailored reconstruction software that selects the best GRAPPA and ghost calibration weights; does 3D rigid‐body realignment with importance weighting; and employs phase correction and complex averaging to lower Rician noise and reduce phase artifacts. For select cases we investigated the use of an additional volume rejection criterion and b‐matrix correction for large motion.

Results:

The DTI image reconstruction procedures developed here were extremely robust in correcting for motion, failing on only three subjects, while providing the radiologists high‐quality data for routine evaluation.

Conclusion:

This work suggests that, apart from the rare instance of continuous motion throughout the scan, high‐quality DTI brain data can be acquired using our proposed integrated sequence and reconstruction that uses a retrospective approach to motion correction. In addition, we demonstrate a substantial improvement in overall image quality by combining phase correction with complex averaging, which reduces the Rician noise that biases noisy data. J. Magn. Reson. Imaging 2012;36:961–971. © 2012 Wiley Periodicals, Inc.     

Compressed‐Sensing multispectral imaging of the postoperative spine

Purpose:

To apply compressed sensing (CS) to in vivo multispectral imaging (MSI), which uses additional encoding to avoid magnetic resonance imaging (MRI) artifacts near metal, and demonstrate the feasibility of CS‐MSI in postoperative spinal imaging.

Materials and Methods:

Thirteen subjects referred for spinal MRI were examined using T2‐weighted MSI. A CS undersampling factor was first determined using a structural similarity index as a metric for image quality. Next, these fully sampled datasets were retrospectively undersampled using a variable‐density random sampling scheme and reconstructed using an iterative soft‐thresholding method. The fully and undersampled images were compared using a 5‐point scale. Prospectively undersampled CS‐MSI data were also acquired from two subjects to ensure that the prospective random sampling did not affect the image quality.

Results:

A two‐fold outer reduction factor was deemed feasible for the spinal datasets. CS‐MSI images were shown to be equivalent or better than the original MSI images in all categories: nerve visualization: P = 0.00018; image artifact: P = 0.00031; image quality: P = 0.0030. No alteration of image quality and T2 contrast was observed from prospectively undersampled CS‐MSI.

Conclusion:

This study shows that the inherently sparse nature of MSI data allows modest undersampling followed by CS reconstruction with no loss of diagnostic quality. J. Magn. Reson. Imaging 2013;37:243–248. © 2012 Wiley Periodicals, Inc.     

Intraprocedural diffusion‐weighted PROPELLER MRI to guide percutaneous biopsy needle placement within rabbit VX2 liver tumors

Purpose

To test the hypothesis that diffusion‐weighted (DW)‐PROPELLER (periodically rotated overlapping parallel lines with enhanced reconstruction) magnetic resonance imaging (MRI) can be used to guide biopsy needle placement during percutaneous interventional procedures to selectively target viable and necrotic tissues within VX2 rabbit liver tumors.

Materials and Methods

Our institutional Animal Care and Use Committee approved all experiments. In six rabbits implanted with 15 VX2 liver tumors, baseline DW‐PROPELLER images acquired prior to the interventional procedure were used for apparent diffusion coefficient (ADC) measurements. Next, intraprocedural DW‐PROPELLER scans were performed with needle position iteratively adjusted to target viable, necrotic, or intermediate border tissue regions. DW‐PROPELLER ADC measurements at the selected needle tip locations were compared with the percentage of tumor necrosis qualitatively assessed at histopathology.

Results

DW‐PROPELLER images demonstrated intratumoral tissue heterogeneity and clearly depicted the needle tip position within viable and necrotic tumor tissues. Mean ADC measurements within the region‐of‐interest encompassing the needle tip were highly correlated with histopathologic tumor necrotic tissue assessments.

Conclusion

DW‐PROPELLER is an effective method to selectively position the biopsy needle tip within viable and necrotic tumor tissues. The DW‐PROPELLER method may offer an important complementary tool for functional guidance during MR‐guided percutaneous procedures. J. Magn. Reson. Imaging 2009;30:366–373. © 2009 Wiley‐Liss, Inc.     

Contrast‐enhanced intracranial magnetic resonance angiography with a spherical shells trajectory and online gridding reconstruction

Purpose:

To evaluate the feasibility of applying the shells trajectory to single‐phase contrast‐enhanced magnetic resonance angiography.

Materials and Methods:

Several methods were developed to overcome the challenges of the clinical implementation of shells including off‐resonance blurring (eg, from lipid signal), aliasing artifacts, and long reconstruction times. These methods included: 1) variable TR with variable readout length to reduce fat signal and off‐resonance blurring; 2) variable sampling density to suppress aliasing artifacts while minimizing acquisition time penalty; and 3) an online 3D gridding algorithm that reconstructed an 8‐channel, 240³ image volume set. Both phantom and human studies were performed to establish the initial feasibility of the methods.

Results:

Phantom and human study results demonstrated the effectiveness of the proposed methods. Shells with variable TR and readout length further suppressed the fat signal compared to the fixed‐TR shells acquisition. Reduced image aliasing was achieved with minimal scan time penalty when a variable sampling density technique was used. The fast online reconstruction algorithm completed in 2 minutes at the scanner console, providing a timely image display in a clinical setting.

Conclusion:

It was demonstrated that the use of the shells trajectory is feasible in a clinical setting to acquire intracranial angiograms with high spatial resolution. Preliminary results demonstrate effective venous suppression in the cavernous sinuses and jugular vein region. J. Magn. Reson. Imaging 2009;30:1101–1109. © 2009 Wiley‐Liss, Inc.     

3D radial sampling and 3D affine transform‐based respiratory motion correction technique for free‐breathing whole‐heart coronary MRA with 100% imaging efficiency

The navigator gating and slice tracking approach currently used for respiratory motion compensation during free‐breathing coronary magnetic resonance angiography (MRA) has low imaging efficiency (typically 30–50%), resulting in long imaging times. In this work, a novel respiratory motion correction technique with 100% scan efficiency was developed for free‐breathing whole‐heart coronary MRA. The navigator signal was used as a reference respiratory signal to segment the data into six bins. 3D projection reconstruction k‐space sampling was used for data acquisition and enabled reconstruction of low resolution images within each respiratory bin. The motion between bins was estimated by image registration with a 3D affine transform. The data from the different respiratory bins was retrospectively combined after motion correction to produce the final image. The proposed method was compared with a traditional navigator gating approach in nine healthy subjects. The proposed technique acquired whole‐heart coronary MRA with 1.0 mm³ isotropic spatial resolution in a scan time of 6.8 ± 0.9 min, compared with 16.2 ± 2.8 min for the navigator gating approach. The image quality scores, and length, diameter and sharpness of the right coronary artery (RCA), left anterior descending coronary artery (LAD), and left circumflex coronary artery (LCX) were similar for both approaches (P > 0.05 for all), but the proposed technique reduced scan time by a factor of 2.5. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Motion corrected intracranial MRA using PROPELLER with RF quadratic encoding

A new motion corrected Time‐of‐Flight MRA technique named Variable Pitch PROPELLER is presented. This technique employs the PROPELLER acquisition and reconstruction scheme for in‐plane bulk motion correction. A non‐ Fourier through‐plane encoding mechanism called quadratic encoding boosts SNR, relative to conventional 2D MRA, in lieu of traditional 3D encoding. Partial Fourier encoding is applied in the slice direction for a further reduction in scan time. This work details the construction and optimization of this technique. VPPROP MRAs are compared with a clinical MOTSA protocol. Initial results show promising robustness to bulk motion effects. The comparisons with MOTSA provide insight as to the additions required to create a comparable scan. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Real‐time flow with fast GPU reconstruction for continuous assessment of cardiac output

Purpose:

To demonstrate the feasibility of real‐time phase contrast magnetic resonance (PCMR) assessment of continuous cardiac output with a heterogeneous (CPU/GPU) system for online image reconstruction.

Materials and Methods:

Twenty healthy volunteers underwent aortic flow examination during exercise using a real‐time spiral PCMR sequence. Acquired data were reconstructed in online fashion using an iterative sensitivity encoding (SENSE) algorithm implemented on an external computer equipped with a GPU card. Importantly, data were sent back to the scanner console for viewing. A multithreaded CPU implementation of the real‐time PCMR reconstruction was used as a reference point for the online GPU reconstruction assessment and validation. A semiautomated segmentation and registration algorithm was applied for flow data analysis.

Results:

There was good agreement between the GPU and CPU reconstruction (?0.4 ± 0.8 mL). There was a significant speed‐up compared to the CPU reconstruction (15×). This translated into the flow data being available on the scanner console ≈9 seconds after acquisition finished. This compares to an estimated time using the CPU implementation of 83 minutes.

Conclusion:

Our heterogeneous image reconstruction system provides a base for translation of complex MRI algorithms into clinical workflow. We demonstrated its feasibility using real‐time PCMR assessment of continuous cardiac output as an example. J. Magn. Reson. Imaging 2012; 36:1477–1482. © 2012 Wiley Periodicals, Inc.

     

Reduction of artifacts in T2‐weighted PROPELLER in high‐field preclinical imaging

A simple technique is implemented for correction of artifacts arising from nonuniform T₂‐weighting of k‐space data in fast spin echo–based PROPELLER (periodically rotated overlapping parallel lines with enhanced reconstruction). An additional blade with no phase‐encoding gradients is acquired to generate the scaling factor used for the correction. Results from simulations and phantom experiments, as well as in vivo experiments in free‐breathing mice, demonstrate the advantages of the proposed method. This technique is developed specifically for high‐field imaging applications where T₂ decay is rapid. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.     

Helium‐3 MR q‐space imaging with radial acquisition and iterative highly constrained back‐projection

An undersampled diffusion‐weighted stack‐of‐stars acquisition is combined with iterative highly constrained back‐projection to perform hyperpolarized helium‐3 MR q‐space imaging with combined regional correction of radiofrequency‐ and T₁‐related signal loss in a single breath‐held scan. The technique is tested in computer simulations and phantom experiments and demonstrated in a healthy human volunteer with whole‐lung coverage in a 13‐sec breath‐hold. Measures of lung microstructure at three different lung volumes are evaluated using inhaled gas volumes of 500 mL, 1000 mL, and 1500 mL to demonstrate feasibility. Phantom results demonstrate that the proposed technique is in agreement with theoretical values, as well as with a fully sampled two‐dimensional Cartesian acquisition. Results from the volunteer study demonstrate that the root mean squared diffusion distance increased significantly from the 500‐mL volume to the 1000‐mL volume. This technique represents the first demonstration of a spatially resolved hyperpolarized helium‐3 q‐space imaging technique and shows promise for microstructural evaluation of lung disease in three dimensions. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

Signal polarity restoration in a 3D inversion recovery sequence used with delayed gadolinium‐enhanced magnetic resonance imaging of cartilage (dGEMRIC)

Purpose:

To develop an image reconstruction algorithm that restores the signal polarity in a three‐dimensional inversion‐recovery (3D‐IR) sequence used in delayed gadolinium‐enhanced MRI of cartilage (dGEMRIC). This approach effectively doubles the dynamic range of data used for T1 curve fitting.

Materials and Methods:

We applied this reconstruction algorithm to a 3D‐IR TFE sequence used for T1 mapping, validated the technique in a phantom study, and performed T1‐map calculations in postosteochondral allograft transplant (OAT) patients. In addition, we performed a signal simulation study to assess the algorithm's capability to reduce the number of inversion times used in the 3D‐IR TFE sequence.

Results:

In comparison to a standard T1‐mapping algorithm that uses the magnitude of the MRI signal, the proposed algorithm improves the reliability of T1 relaxation fits to the inversion‐recovery three‐parameter function. The signal simulation study shows that the number of TI inversion times can be reduced to as few as four, without compromising the accuracy of T1 calculations.

Conclusion:

This algorithm can be applied to any 2D‐ or 3D‐IR acquisition sequence used in conjunction with dGEMRIC. Application of the algorithm improves the reliability of T1 calculations and allows the number of TIs to be reduced, leading to shorter scan times in dGEMRIC. J. Magn. Reson. Imaging 2012;36:1248–1255. © 2012 Wiley Periodicals, Inc.     

Rosette spectroscopic imaging: Optimal parameters for alias‐free,high sensitivity spectroscopic imaging

Purpose

To optimize the Rosette trajectories for fast, high sensitivity spectroscopic imaging experiments and to compare this acquisition technique with other chemical shift imaging (CSI) methods.

Materials and Methods

A framework for comparing the sensitivity of the Rosette Spectroscopic Imaging (RSI) acquisition to other spectroscopic imaging experiments is outlined. Accounting for hardware constraints, trajectory parameters that provide for optimal sampling and minimal artifact production are found. Along with an analytical expression for the number of excitations to be used in an RSI experiment that is provided, the theoretical precompensation weights used for optimal image reconstruction are derived.

Results

The spectral response function for RSI is shown to be approximately the same as the point spread function of standard Fourier reconstructions. While the signal‐to‐noise ratio (SNR) for an RSI experiment is reduced by the inherent nonuniform sampling of these trajectories, their circular k‐space support and speed of spatial encoding leads to greater SNR efficiency and improvements in the total data acquisition time relative to the gold standard CSI approach with square k‐space support and to similar efficiency to spiral CSI acquisitions. Numerical simulations and in vivo experimental data are presented to demonstrate the properties of this data acquisition technique.

Conclusion

This work demonstrates the use of Rosette trajectories and how to achieve improved efficiency for these trajectories in a two‐dimensional spectroscopic imaging experiment. J. Magn. Reson. Imaging 2009;29:1375–1385. © 2009 Wiley‐Liss, Inc.     

Accelerating three‐dimensional molecular cardiovascular MR imaging using compressed sensing

Purpose:

To accelerate the acquisition of three‐dimensional (3D) high‐resolution cardiovascular molecular MRI by using Compressed Sensing (CS) reconstruction.

Materials and Methods:

Molecular MRI is an emerging technique for the early assessment of cardiovascular disease. This technique provides excellent soft tissue differentiation at a molecular and cellular level using target‐specific contrast agents (CAs). However, long scan times are required for 3D molecular MRI. Parallel imaging can be used to speed‐up these acquisitions, but hardware considerations limit the maximum acceleration factor. This limitation is important in small‐animal studies, where single‐coils are commonly used. Here we exploit the sparse nature of molecular MR images, which are characterized by localized and high‐contrast biological target‐enhancement, to accelerate data acquisition. CS was applied to detect: (a) venous thromboembolism and (b) coronary injury and aortic vessel wall in single‐ and multiple‐coils acquisitions, respectively.

Results:

Retrospective undersampling showed good overall image quality with accelerations up to four for thrombus and aortic images, and up to three for coronary artery images. For higher acceleration factors, features with high CA uptake were still well recovered while low affinity targets were less preserved with increased CS undersampling artifacts. Prospective undersampling was performed in an aortic image with acceleration of two, showing good contrast and well‐defined tissue boundaries in the contrast‐enhanced regions.

Conclusion:

We demonstrate the successful application of CS to preclinical molecular MR with target specific gadolinium‐based CAs using retrospective (accelerations up to four) and prospective (acceleration of two) undersampling. J. Magn. Reson. Imaging 2012; 36:1362–1371. © 2012 Wiley Periodicals, Inc.     

MRI reconstruction from 2D truncated k-space

Purpose:

To shorten acquisition time by means of both partial scanning and partial echo acquisition and to reconstruct images from such 2D partial k‐space acquisitions.

Materials and Methods:

We propose an approach to reconstructing magnetic resonance images from 2D truncated k‐space in which the k‐space is truncated in both phase‐ and frequency‐encoding directions. Unlike conventional reconstruction techniques, the proposed approach is based on a newly developed 2D singularity function analysis (SFA) model and a sparse representation of an image whose parameters can be estimated from the 2D partial k‐space data. Such a sparse representation leads to an accurate recovery of the missing k‐space data and, hence, an accurate reconstruction of the image.

Results:

The proposed approach can reconstruct an image from as little as 20%–30% of the k‐space data and the quality of the reconstructed image is comparable to the reference image that is reconstructed from the complete k‐space data.

Conclusion:

Despite the high asymmetry of a 2D truncated k‐space, the proposed approach allows for accurate reconstruction without the need of phase correction and, thus, overcomes the assumption of slow phase variations that is usually required by the existing reconstruction methods. It provides a new way of fast imaging for applications that require a significant reduction of the acquisition time. J. Magn. Reson. Imaging 2012;35:1196‐1206. © 2011 Wiley Periodicals, Inc.     

Multishot PROPELLER for high‐field preclinical MRI

With the development of numerous mouse models of cancer, there is a tremendous need for an appropriate imaging technique to study the disease evolution. High‐field T₂‐weighted imaging using PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) MRI meets this need. The two‐shot PROPELLER technique presented here provides (a) high spatial resolution, (b) high contrast resolution, and (c) rapid and noninvasive imaging, which enables high‐throughput, longitudinal studies in free‐breathing mice. Unique data collection and reconstruction makes this method robust against motion artifacts. The two‐shot modification introduced here retains more high‐frequency information and provides higher signal‐to‐noise ratio than conventional single‐shot PROPELLER, making this sequence feasible at high fields, where signal loss is rapid. Results are shown in a liver metastases model to demonstrate the utility of this technique in one of the more challenging regions of the mouse, which is the abdomen. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

SPIRiT: Iterative self‐consistent parallel imaging reconstruction from arbitrary k‐space

A new approach to autocalibrating, coil‐by‐coil parallel imaging reconstruction, is presented. It is a generalized reconstruction framework based on self‐consistency. The reconstruction problem is formulated as an optimization that yields the most consistent solution with the calibration and acquisition data. The approach is general and can accurately reconstruct images from arbitrary k‐space sampling patterns. The formulation can flexibly incorporate additional image priors such as off‐resonance correction and regularization terms that appear in compressed sensing. Several iterative strategies to solve the posed reconstruction problem in both image and k‐space domain are presented. These are based on a projection over convex sets and conjugate gradient algorithms. Phantom and in vivo studies demonstrate efficient reconstructions from undersampled Cartesian and spiral trajectories. Reconstructions that include off‐resonance correction and nonlinear ?₁‐wavelet regularization are also demonstrated. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.