POCSENSE: POCS-based reconstruction for sensitivity encoded magnetic resonance imaging.

A novel method for iterative reconstruction of images from undersampled MRI data acquired by multiple receiver coil systems is presented. Based on Projection onto Convex Sets (POCS) formalism, the method for SENSitivity Encoded data reconstruction (POCSENSE) can be readily modified to include various linear and nonlinear reconstruction constraints. Such constraints may be beneficial for reconstructing highly and overcritically undersampled data sets to improve image quality. POCSENSE is conceptually simple and numerically efficient and can reconstruct images from data sampled on arbitrary k-space trajectories. The applicability of POCSENSE for image reconstruction with nonlinear constraining was demonstrated using a wide range of simulated and real MRI data.     

x-f Choice: reconstruction of undersampled dynamic MRI by data-driven alias rejection applied to contrast-enhanced angiography.

A technique for reconstructing dynamic undersampled MRI data, termed "x-f choice," was developed and applied to dynamic contrast-enhanced MR angiography (DCE-MRA). Regular undersampling in k-t space (a hybrid of k-space and time) creates aliasing in the conjugate x-f space that must be resolved. When regions in the object containing fast dynamic change are sparse, as in DCE-MRA, signal overlap caused by aliasing is often much less than the undersample factor would imply. x-f Choice reconstruction identifies overlapping signals using a model of the full non-aliased x-f space that is automatically generated from the undersampled data, and applies parallel imaging (PI) to separate them. No extra reference scans are required to generate either the model or the coil sensitivity maps. At each location in the reconstructed images, g-factor noise amplification is compared with predicted reconstruction errors to obtain an optimized solution. Acceleration factors greater than the number of receiver coils are possible, but are limited by the sparseness of the dynamic content and the signal-to-noise ratio (SNR) (in DCE-MRA the latter is dominant). Temporal fidelity was validated for up to a factor 10 speed-up using retrospectively undersampled data from a six-coil array. The method was tested on volunteers using fivefold prospective undersampling.     

Parallel magnetic resonance imaging with adaptive radius in k-space (PARS): constrained image reconstruction using k-space locality in radiofrequency coil encoded data.

A parallel image reconstruction algorithm is presented that exploits the k-space locality in radiofrequency (RF) coil encoded data. In RF coil encoding, information relevant to reconstructing an omitted datum rapidly diminishes as a function of k-space separation between the omitted datum and the acquired signal data. The proposed method, parallel magnetic resonance imaging with adaptive radius in k-space (PARS), harnesses this physical property of RF coil encoding via a sliding-kernel approach. Unlike generalized parallel imaging approaches that might typically involve inverting a prohibitively large matrix for arbitrary sampling trajectories, the PARS sliding-kernel approach creates manageable and distributable independent matrices to be inverted, achieving both computational efficiency and numerical stability. An empirical method designed to measure total error power is described, and the total error power of PARS reconstructions is studied over a range of k-space radii and accelerations, revealing "minimal-error" conditions at comparatively modest k-space radii. PARS reconstructions of undersampled in vivo Cartesian and non-Cartesian data sets are shown and are compared selectively with traditional SENSE reconstructions. Various characteristics of the PARS k-space locality constraint (such as the tradeoff between signal-to-noise ratio and artifact power and the relationship with iterative parallel conjugate gradient approaches or nonparallel gridding approaches) are discussed.     

Localization by nonlinear phase preparation and k-space trajectory design

A technique is described to localize MR signals from a target volume using nonlinear pulsed magnetic fields and spatial encoding trajectories designed using local k-space theory. The concept of local k-space is outlined theoretically, and this principle is applied to simulated phantom and cardiac MRI data in the presence of surface and quadrupolar gradient coil phase modulation. Phantom and in vivo human brain images are obtained using a custom, high-performance quadrupolar gradient coil integrated with a whole-body 3-T MRI system to demonstrate target localization using three-dimensional T 2*-weighted spoiled gradient echo, two-dimensional segmented, multiple gradient encoded spin echo, and three-dimensional balanced steady-state free precession acquisitions. This method may provide a practical alternative to selective radiofrequency excitation at ultra-high-field, particularly for steady-state applications where repetition time (TR) must be minimized and when the amount of energy deposited in human tissues is prohibitive. There are several limitations to the approach including the spatial variation in resolution, high frequency aliasing artifacts, and spatial variation in echo times and contrast.     

Varying kernel-extent gridding reconstruction for undersampled variable-density spirals.

Nonuniform, non-Cartesian k-space trajectories enable fast scanning with reduced motion and flow artifacts. In such cases, the data are usually convolved with a kernel and resampled onto a Cartesian grid before reconstruction. For trajectories such as undersampled variable-density spirals, the mainlobe width of the kernel for undersampled high spatial frequencies has to be larger to limit the amount of aliasing energy. Continuously varying the kernel extent is time consuming. By dividing k-space into several annuli and using appropriate mainlobe widths for each, the aliasing energy and noise can be reduced at the expense of lower resolution towards the edge of the field of view (FOV). Resolution can instead be preserved at the center of the FOV, which is expected to be free of artifacts, without any artifact reduction. The image reconstructed from each annulus can be deapodized separately. The method can be applied to most k-space trajectories used in MRI.     

An optimized center-out k-space trajectory for multishot MRI: comparison with spiral and projection reconstruction.

A method for collecting MRI data on a set of rotated trajectories that begin at the center of k-space is outlined. It is theoretically slightly faster, slightly less susceptible to off-resonance and motion-induced phase, and produces images with slightly better signal-to-noise ratio than methods using Archimedean spiral trajectories, particularly for a short sampling duration. It also produces more accurate images than those of projection reconstruction methods, which are significantly undersampled azimuthally. This method may be most useful when imaging areas with large inhomogeneities (e.g., near metallic implants), short T(2) species, or high turbulence (e.g., gas imaging). Magn Reson Med 42:714-720, 1999.     

Fast T(1) mapping with volume coverage.

Four different sequences which enable high-resolution, multislice T(1) relaxation-time mapping are presented. All these sequences are based on the Look-Locker method with differences arising from the use of either a saturation-recovery or inversion-recovery module prior to data acquisition with a full k-space or banded k-space acquisition scheme. The methods were implemented on a standard clinical scanner and the accuracy of the T(1) results was evaluated against spectroscopic measurements. The accuracy of the T(1) maps validated by phantom imaging measurements is around 1% for species which relax with T(1) times that mimic gray/white matter (T(1) < or = 1000 ms). Additionally, the inherent multislice, multipoint capability of the methods is demonstrated. Finally, in vivo results of the human brain obtained using the faster method are presented. The fastest data acquisition was achieved with a saturation-recovery, banded k-space method where k-space was divided into three segments; an overall acquisition time of around 5 min (for species with T(1) < or = 1 sec) was achieved for a T(1) map which can, in principle, provide whole-brain coverage with a matrix size of 256 x 256 at multiple time-points. Magn Reson Med 46:131-140, 2001.     

Sampling density compensation in MRI: rationale and an iterative numerical solution.

Data collection of MRI which is sampled nonuniformly in k-space is often interpolated onto a Cartesian grid for fast reconstruction. The collected data must be properly weighted before interpolation, for accurate reconstruction. We propose a criterion for choosing the weighting function necessary to compensate for nonuniform sampling density. A numerical iterative method to find a weighting function that meets that criterion is also given. This method uses only the coordinates of the sampled data; unlike previous methods, it does not require knowledge of the trajectories and can easily handle trajectories that "cross" in k-space. Moreover, the method can handle sampling patterns that are undersampled in some regions of k-space and does not require a post-gridding density correction. Weighting functions for various data collection strategies are shown. Synthesized and collected in vivo data also illustrate aspects of this method.     

EPI image reconstruction with correction of distortion and signal losses

PURPOSE: To derive and implement a method for correcting geometric distortions and recovering magnetic resonance imaging (MRI) signal losses caused by susceptibility-induced magnetic field gradients (SFGs) in regions with large static field inhomogeneities in echo-planar imaging (EPI). MATERIALS AND METHODS: Factors to account for field inhomogeneities and SFGs were added in a traditional EPI equation that was a simple Fourier transform (FT) for expressing the actual k-space data of an EPI scan. The inverse calculation of this "distorted EPI" equation was used as a kernel to correct geometric distortions and reductions in intensity during reconstruction. A step-by-step EPI reconstruction method was developed to prevent complicated phase unwrapping problems. Some EPI images of phantom and human brains were reconstructed from standard EPI k-spaces. RESULTS: All images were reconstructed using the proposed multistep method. Geometric distortions were corrected and SFG-induced MRI signal losses were recovered. CONCLUSION: Results suggest that applying our method for reconstructing EPI images to reduce distortions and MRI signal losses is feasible.     

UNFOLD using a temporal subtraction and spectral energy comparison technique.

In dynamic MRI, several methods have been demonstrated to increase acquisition speed by decreasing the number of sequential phase encodings. The UNFOLD technique interleaves the measurements of k-space, reconstructs aliased images from each k-space interleaf, and applies a temporal low-pass filter to obtain the nonaliased images. However, low-pass filter resolution of the nonaliased images fails if there is overlap between the spatially aliased temporal spectra. In this study a subtraction method was used to remove the static portion of the image. The aliased and nonaliased dynamic portions are then resolved by comparing the temporal energy of bands in the power spectrum. This method was combined with the 3D 2 x 2 UNFOLD (a factor of 2 interleaves in two directions) technique. The combination resulted in a factor of 4 improvement in acquisition speed. Application of this method to a time-resolved, contrast-enhanced flow phantom study is presented.     

Reduced aliasing artifacts using variable-density k-space sampling trajectories.

A variable-density k-space sampling method is proposed to reduce aliasing artifacts in MR images. Because most of the energy of an image is concentrated around the k-space center, aliasing artifacts will contain mostly low-frequency components if the k-space is uniformly undersampled. On the other hand, because the outer k-space region contains little energy, undersampling that region will not contribute severe aliasing artifacts. Therefore, a variable-density trajectory may sufficiently sample the central k-space region to reduce low-frequency aliasing artifacts and may undersample the outer k-space region to reduce scan time and to increase resolution. In this paper, the variable-density sampling method was implemented for both spiral imaging and two-dimensional Fourier transform (2DFT) imaging. Simulations, phantom images and in vivo cardiac images show that this method can significantly reduce the total energy of aliasing artifacts. In general, this method can be applied to all types of k-space sampling trajectories.     

Self-calibrating GRAPPA operator gridding for radial and spiral trajectories.

Self-calibrating GRAPPA operator gridding (GROG) is a method by which non-Cartesian MRI data can be gridded using spatial information from a multichannel coil array without the need for an additional calibration dataset. Using self-calibrating GROG, the non-Cartesian datapoints are shifted to nearby k-space locations using parallel imaging weight sets determined from the datapoints themselves. GROG employs the GRAPPA Operator, a special formulation of the general reconstruction method GRAPPA, to perform these shifts. Although GROG can be used to grid undersampled datasets, it is important to note that this method uses parallel imaging only for gridding, and not to reconstruct artifact-free images from undersampled data. The innovation introduced here, namely, self-calibrating GROG, allows the shift operators to be calculated directly out of the non-Cartesian data themselves. This eliminates the need for an additional calibration dataset, which reduces the imaging time and also makes the GROG reconstruction more robust by removing possible inconsistencies between the calibration and non-Cartesian datasets. Simulated and in vivo examples of radial and spiral datasets gridded using self-calibrating GROG are compared to images gridded using the standard method of convolution gridding.     

High-resolution diffusion-weighted imaging with interleaved variable-density spiral acquisitions

PURPOSE: To develop a multishot magnetic resonance imaging (MRI) pulse sequence and reconstruction algorithm for diffusion-weighted imaging (DWI) in the brain with submillimeter in-plane resolution. MATERIALS AND METHODS: A self-navigated multishot acquisition technique based on variable-density spiral k-space trajectory design was implemented on clinical MRI scanners. The image reconstruction algorithm takes advantage of the oversampling of the center k-space and uses the densely sampled central portion of the k-space data for both imaging reconstruction and motion correction. The developed DWI technique was tested in an agar gel phantom and three healthy volunteers. RESULTS: Motions result in phase and k-space shifts in the DWI data acquired using multishot spiral acquisitions. With the two-dimensional self-navigator correction, diffusion-weighted images with a resolution of 0.9 x 0.9 x 3 mm3 were successfully obtained using different interleaves ranging from 8-32. The measured apparent diffusion coefficient (ADC) in the homogenous gel phantom was (1.66 +/- 0.09) x 10(-3) mm2/second, which was the same as measured with single-shot methods. The intersubject average ADC from the brain parenchyma of normal adults was (0.91 +/- 0.01) x 10(-3) mm2/second, which was in a good agreement with the reported literature values. CONCLUSION: The self-navigated multishot variable-density spiral acquisition provides a time-efficient approach to acquire high-resolution diffusion-weighted images on a clinical scanner. The reconstruction algorithm based on motion correction in the k-space data is robust, and measured ADC values are accurate and reproducible.     

Temporal filtering effects in dynamic parallel MRI

Autocalibrated parallel MRI methods such as TSENSE or k‐t SENSE have been presented for dynamic imaging studies as they are able to provide images with high temporal resolution. One key element of these techniques is the temporal averaging of the undersampled raw data to obtain an unaliased image. This image represents the temporal average (also known as direct current, DC) and is used to derive the reconstruction parameters. In this work, we show that aliasing artifacts can be introduced in the DC signal obtained from the undersampled raw data. These artifacts lead to undesired temporal filtering effects when the DC signal is used for coil sensitivity calibration or when the DC signal is subtracted from the raw data. It is demonstrated that the temporal filtering effects can be reduced significantly by filtering the DC signal. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Shared k-space echo planar imaging with keyhole.

Time-dependent phenomena are of great interest, and researchers have sought to shed light on these processes with MRI, particularly in vivo. In this work, a new hybrid technique based on EPI and using the concept of keyhole imaging is presented. By sharing peripheral k-space data between images and acquiring the keyhole more frequently, it is shown that the spatial resolution of the reconstructed images can be maintained. The method affords a higher temporal resolution and is more robust against susceptibility and chemical-shift artifacts than single-shot EPI. The method, termed shared k-space echo planar imaging with keyhole (shared EPIK), has been implemented on a standard clinical scanner. Technical details, simulation results, phantom images, in vivo images, and fMRI results are presented. These results indicate that the new method is robust and may be used for dynamic MRI applications. Magn Reson Med 45:109-117, 2001.     

Parallel imaging reconstruction using automatic regularization.

Increased spatiotemporal resolution in MRI can be achieved by the use of parallel acquisition strategies, which simultaneously sample reduced k-space data using the information from multiple receivers to reconstruct full-FOV images. The price for the increased spatiotemporal resolution in parallel MRI is the degradation of the signal-to-noise ratio (SNR) in the final reconstructed images. Part of the SNR reduction results when the spatially correlated nature of the information from the multiple receivers destabilizes the matrix inversion used in the reconstruction of the full-FOV image. In this work, a reconstruction algorithm based on Tikhonov regularization is presented that reduces the SNR loss due to geometric correlations in the spatial information from the array coil elements. Reference scans are utilized as a priori information about the final reconstructed image to provide regularized estimates for the reconstruction using the L-curve technique. This automatic regularization method reduces the average g-factors in phantom images from a two-channel array from 1.47 to 0.80 in twofold sensitivity encoding (SENSE) acceleration. In vivo anatomical images from an eight-channel system show an averaged g-factor reduction of 1.22 to 0.84 in 2.67-fold acceleration.     

Dynamic MRI with projection reconstruction and KWIC processing for simultaneous high spatial and temporal resolution.

A method for dynamic imaging in MRI is presented that enables the acquisition of a series of images with both high temporal and high spatial resolution. The technique, which is based on the projection reconstruction (PR) imaging scheme, utilizes distinct data acquisition and reconstruction strategies to achieve this simultaneous capability. First, during acquisition, data are collected in multiple undersampled passes, with the view angles interleaved in such a way that those of subsequent passes bisect the views of earlier ones. During reconstruction, these views are weighted according to a previously described k-space weighted image contrast (KWIC) technique that enables the manipulation of image contrast by selective filtering. Unlike conventional undersampled PR methods, the proposed dynamic KWIC technique does not suffer from low image SNR or image degradation due to streaking artifacts. The effectiveness of dynamic KWIC is demonstrated in both simulations and in vivo, high-resolution, contrast-enhanced imaging of breast lesions.     

Reconstruction of undersampled non-Cartesian data sets using pseudo-Cartesian GRAPPA in conjunction with GROG.

Most k-space-based parallel imaging reconstruction techniques, such as Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA), necessitate the acquisition of regularly sampled Cartesian k-space data to reconstruct a nonaliased image efficiently. However, non-Cartesian sampling schemes offer some inherent advantages to the user due to their better coverage of the center of k-space and faster acquisition times. On the other hand, these sampling schemes have the disadvantage that the points acquired generally do not lie on a grid and have complex k-space sampling patterns. Thus, the extension of Cartesian GRAPPA to non-Cartesian sequences is nontrivial. This study introduces a simple, novel method for performing Cartesian GRAPPA reconstructions on undersampled non-Cartesian k-space data gridded using GROG (GRAPPA Operator Gridding) to arrive at a nonaliased image. Because the undersampled non-Cartesian data cannot be reconstructed using a single GRAPPA kernel, several Cartesian patterns are selected for the reconstruction. This flexibility in terms of both the appearance and number of patterns allows this pseudo-Cartesian GRAPPA to be used with undersampled data sets acquired with any non-Cartesian trajectory. The successful implementation of the reconstruction algorithm using several different trajectories, including radial, rosette, spiral, one-dimensional non-Cartesian, and zig-zag trajectories, is demonstrated.     

Undersampling k-space using fast progressive 3D trajectories.

In 3D MRI, sampling k-space with traditional trajectories can be excessively time-consuming. Fast imaging trajectories are used in an attempt to efficiently cover the k-space and reduce the scan time without significantly affecting the image quality. In many applications, further reductions in scan time can be achieved via undersampling of the k-space; however, no clearly optimal method exists. In most 3D trajectories the k-space is divided into regions that are sampled with shots that share a common geometry (e.g., spirals). A different approach is to design trajectories that gradually but uniformly cover the k-space. In the current work, successive shots progressively add sampled regions to the 3D frequency space. By cutting the sequence short, a natural undersampled method is obtained. This can be particularly efficient because in these types of trajectories the contribution of new information by later shots is less significant. In this work the performance of progressive trajectories for different degrees of undersampling is assessed with trajectories based on missile guidance (MG) ideas. The results show that the approach can be efficient in terms of reducing the scan time, and performs better than the stack of spirals (SOS) technique, particularly under nonideal conditions.