Phase correction-based singularity function analysis for partial k-space reconstruction

Partial k-space acquisition is a conventional method in magnetic resonance imaging (MRI) for reducing imaging time while maintaining image quality. In this field, image reconstruction from partial k-space is a key issue. This paper proposes an approach fundamentally different from traditional techniques for reconstructing magnetic resonance (MR) images from partial k-space. It uses a so-called singularity function analysis (SFA) model based on phase correction. With such a reconstruction approach, some nonacquired negative spatial frequencies are first recovered by means of phase correction and Hermitian symmetry property, and then the other nonacquired negative and/or positive spatial frequencies are estimated using the mathematical SFA model. The method is particularly suitable for asymmetrical partial k-space acquisition owing to its ability of overcoming reconstruction limitations due to k-space truncations. The performance of this approach is evaluated using both simulated and real MR brain images, and compared with existing techniques. The results demonstrate that the proposed SFA based on phase correction achieves higher image quality than the initial SFA or the projection-onto-convex sets (POCS) method.     

MR image reconstruction of sparsely sampled 3D k-space data by projection-onto-convex sets

In many rapid three-dimensional (3D) magnetic resonance (MR) imaging applications, such as when following a contrast bolus in the vasculature using a moving table technique, the desired k-space data cannot be fully acquired due to scan time limitations. One solution to this problem is to sparsely sample the data space. Typically, the central zone of k-space is fully sampled, but the peripheral zone is partially sampled. We have experimentally evaluated the application of the projection-onto-convex sets (POCS) and zero-filling (ZF) algorithms for the reconstruction of sparsely sampled 3D k-space data. Both a subjective assessment (by direct image visualization) and an objective analysis [using standard image quality parameters such as global and local performance error and signal-to-noise ratio (SNR)] were employed. Compared to ZF, the POCS algorithm was found to be a powerful and robust method for reconstructing images from sparsely sampled 3D k-space data, a practical strategy for greatly reducing scan time. The POCS algorithm reconstructed a faithful representation of the true image and improved image quality with regard to global and local performance error, with respect to the ZF images. SNR, however, was superior to ZF only when more than 20% of the data were sparsely sampled. POCS-based methods show potential for reconstructing fast 3D MR images obtained by sparse sampling.     

Accelerated passive MR catheter tracking into the carotid artery of canines

Background

Using magnetic resonance (MR) imaging for navigating catheters has several advantages when compared with the current “gold standard” modality of X-ray imaging. A significant drawback to interventional MR is inferior temporal and spatial resolutions, as high spatial resolution images cannot be collected and displayed at rates equal to X-ray imaging. In particular, passive MR catheter tracking experiments that use positive contrast mechanisms have poor temporal imaging rates and signal-to-noise ratio. As a result, with passive methods, it is often difficult to reconstruct motion artifact-free tracking images from areas with motion, such as the thoracic cavity.

Methods

In this study, several accelerated MR acquisition strategies, including parallel imaging and compressed sensing (CS), were evaluated to determine which method is most effective at improving the frame rate and passive detection of catheters in regions of physiological motion. Device navigation was performed both in vitro, through the aortic arch of an anthropomorphic chest phantom, and in vivo from the femoral artery, up the descending aorta into the supra-aortic branching vessels in canines.

Results and Discussion

The different parallel imaging methods produced images of low quality. CS with a two-fold acceleration was found to be the most effective method for generating tracking images, improving the image frame rate to 5.2 Hz, while maintaining a relatively high in-plane resolution. Using CS, motion artifact was decreased and the catheters were visualized with good conspicuity near the heart.

Conclusions

The improvement in the imaging frame rate by image acceleration was sufficient to overcome motion artifacts and to better visualize catheters in the thoracic cavity with passive tracking. CS preformed best at tracking. Navigation with passive MR catheter tracking was demonstrated from the femoral artery to the carotid artery in canines.     

K-space trajectory mapping and its application for ultrashort Echo time imaging

MR images are affected by system delays and gradient field imperfections which induce discrepancies between prescribed and actual k-space trajectories. This could be even more critical for non-Cartesian data acquisitions where even a small deviation from the assumed k-space trajectory results in severe image degradation and artifacts. Knowledge of the actual k-space trajectories is therefore crucial and can be incorporated in the reconstruction of high quality non-Cartesian images. A novel MR method for the calibration of actual gradient waveforms was developed using a combination of phase encoding increments and subsequent detection of the exact time point at which the corresponding trajectory is crossing the k-space origin. The measured sets of points were fitted to a parametrical model to calculate the complete actual acquisition trajectory. Measurements performed on phantoms and volunteers, positioned both in- and off-isocenter of the magnet, clearly demonstrate the improvement in reconstructed ultrashort echo time (UTE) images, when information from calibration of k-space sampling trajectories is employed in the MR image reconstruction procedure. The unique feature of the proposed method is its robustness and simple experimental setup, making it suitable for quick acquisition trajectory calibration procedures e.g. for non-Cartesian radial fast imaging.     

Centric scan SPRITE magnetic resonance imaging: optimization of SNR, resolution, and relaxation time mapping

Two strategies for the optimization of centric scan SPRITE (single point ramped imaging with T1 enhancement) magnetic resonance imaging techniques are presented. Point spread functions (PSF) for the centric scan SPRITE methodologies are numerically simulated, and the blurring manifested in a centric scan SPRITE image through PSF convolution is characterized. Optimal choices of imaging parameters and k-space sampling scheme are predicted to obtain maximum signal-to-noise ratio (SNR) while maintaining acceptable image resolution. The point spread function simulation predictions are verified experimentally. The acquisition of multiple FID points following each RF excitation is described and the use of the Chirp z-Transform algorithm for the scaling of field of view (FOV) of the reconstructed images is illustrated. Effective recombination of the rescaled images for SNR improvement and T*2 mapping is demonstrated.     

Motion artifact reduction technique for dual-contrast FSE imaging

There is considerable similarity between proton density-weighted (PDw) and T2-weighted (T2w) images acquired by dual-contrast fast spin-echo (FSE) sequences. The similarity manifests itself in image space as consistency between the phases of PDw and T2w images and in k-space as correspondence between PDw and T2w k-space data. A method for motion artifact reduction for dual-contrast FSE imaging has been developed. The method uses projection onto convex sets (POCS) formalism and is based on image space phase consistency and the k-space similarity between PDw and T2w images. When coupled with a modified dual-contrast FSE phase encoding scheme the method can yield considerable artifact reduction, as long as less than half of the acquired data is corrupted by motion. The feasibility and efficiency of the developed method were demonstrated using phantom and human MRI data.     

Compressed Sensing MRI Using Sparsity Averaging and FISTA

Magnetic resonance imaging (MRI) is widely adopted for clinical diagnosis due to its non-invasively detection. However, acquisition of full k-space data limits its imaging speed. Compressed sensing (CS) provides a new technique to significantly reduce the measurements with high-quality MR image reconstruction. The sparsity of the MR images is one of the crucial bases of CS-MRI. In this paper, we present to use sparsity averaging prior for CS-MRI reconstruction in the basis of that MR images have average sparsity over multiple wavelet frames. The problem is solved using a Fast Iterative Shrinkage Thresholding Algorithm (FISTA), each iteration of which includes a shrinkage step. The performance of the proposed method is evaluated for several types of MR images. The experiment results illustrate that our approach exhibits a better performance than those methods that using redundant frame or a single orthonormal basis to promote sparsity.     

k-space inherited parallel acquisition (KIPA): application on dynamic magnetic resonance imaging thermometry

In this study, a novel method for dynamic parallel image acquisition and reconstruction is presented. In this method, called k-space inherited parallel acquisition (KIPA), localized reconstruction coefficients are used to achieve higher reduction factors, and lower noise and artifact levels compared to that of generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction. In KIPA, the full k-space for the first frame and the partial k-space for later frames are required to reconstruct a whole series of images. Reconstruction coefficients calculated for different segments of k-space from the first frame data set are used to estimate missing k-space lines in corresponding k-space segments of other frames. The local determination of KIPA reconstruction coefficients is essential to adjusting them according to the local signal-to-noise ratio characteristics of k-space data. The proposed algorithm is applicable to dynamic imaging with arbitrary k-space sampling trajectories. Simulations of magnetic resonance thermometry using the KIPA method with a reduction factor of 6 and using dynamic imaging studies of human subjects with reduction factors of 4 and 6 have been performed to prove the feasibility of our method and to show apparent improvement in image quality in comparison with GRAPPA for dynamic imaging.     

Diffusion-weighted three-dimensional MP-RAGE MR imaging

The advantages of three-dimensional (3D) acquisition are that you obtain thinner and more slices with better profiles, and better signal-to-noise ratio for an equivalent slice thickness. Three-dimensional acquisition is preferable for obtaining contiguous thin-slice MR images. However, the acquisition time extends compared with the two-dimensional acquisition because the second phase-encode axis is applied by the 3D acquisition. Therefore, 3D acquisition should be a high-speed imaging method. In this paper, a new diffusion-sensitive 3D magnetization-prepared rapid gradient-echo (3D MP-RAGE) sequence was studied. In this sequence, a preparation phase with a 90 degrees RF-motion proving gradient (MPG): MPG-180 degrees RF-MPG-90 degrees RF pulse train (diffusion-weighted driven-equilibrium Fourier transform) was used to sensitize the magnetization to diffusion. Centric k-space acquisition order is necessary to minimize saturation effects from tissues with short relaxation times. From phantom experimental results, the effect of the diffusion weighting was changed by the centric vs. sequential k-space acquisition order. The effect of centric k-space acquisition order was larger than the effect of sequential k-space acquisition order. The contrast of centric k-space acquisition order became equal to the contrast of conventional diffusion-weighted spin echo. From rat experimental results, small isotropic diffusion-weighted image data (voxel size: 0.625 x 0.625 x 0.625 mm3) were obtained. This sequence was useful in vivo.     

Motion correction based reconstruction method for compressively sampled cardiac MR imaging

Respiratory motion during Magnetic Resonance (MR) acquisition causes strong blurring artifacts in the reconstructed images. These artifacts become more pronounced when used with the fast imaging reconstruction techniques like compressed sensing (CS). Recently, an MR reconstruction technique has been done with the help of compressed sensing (CS), to provide good quality sparse images from the highly under-sampled k-space data. In order to maximize the benefits of CS, it is obvious to use CS with the motion corrected samples. In this paper, we propose a novel CS based motion corrected image reconstruction technique. First, k-space data have been assigned to different respiratory state with the help of frequency domain phase correlation method. Then, multiple sparsity constraints has been used to provide good quality reconstructed cardiac cine images with the highly under-sampled k-space data. The proposed method exploits the multiple sparsity constraints, in combination with demon based registration technique and a novel reconstruction technique to provide the final motion free images. The proposed method is very simple to implement in clinical settings as compared to existing motion corrected methods. The performance of the proposed method is examined using simulated data and clinical data. Results show that this method performs better than the reconstruction of CS based method of cardiac cine images. Different acceleration rates have been used to show the performance of the proposed method.     

Methods for quantitative image quality evaluation of MRI parallel reconstructions: detection and perceptual difference model

Many reconstruction algorithms are being proposed for parallel magnetic resonance imaging (MRI), which uses multiple coils and subsampled k-space data, and a quantitative method for comparison of algorithms is sorely needed. On such images, we compared three methods for quantitative image quality evaluation: human detection, computer detection model and a computer perceptual difference model (PDM). One-quarter sampling and three different reconstruction methods were investigated: a regularization method developed by Ying et al., a simplified regularization method and an iterative method proposed by Pruessmann et al. Images obtained from a full complement of k-space data were also included as reference images. Detection studies were performed using a simulated dark tumor added on MR images of fresh bovine liver. Human detection depended strongly on reconstruction methods used, with the two regularization methods achieving better performance than the iterative method. Images were also evaluated using detection by a channelized Hotelling observer model and by PDM scores. Both predicted the same trends as observed from human detection. We are encouraged that PDM gives trends similar to that for human detection studies. Its ease of use and applicability to a variety of MRI situations make it attractive for evaluating image quality in a variety of MR studies.     

Exploiting the wavelet structure in compressed sensing MRI

Sparsity has been widely utilized in magnetic resonance imaging (MRI) to reduce k-space sampling. According to structured sparsity theories, fewer measurements are required for tree sparse data than the data only with standard sparsity. Intuitively, more accurate image reconstruction can be achieved with the same number of measurements by exploiting the wavelet tree structure in MRI. A novel algorithm is proposed in this article to reconstruct MR images from undersampled k-space data. In contrast to conventional compressed sensing MRI (CS-MRI) that only relies on the sparsity of MR images in wavelet or gradient domain, we exploit the wavelet tree structure to improve CS-MRI. This tree-based CS-MRI problem is decomposed into three simpler subproblems then each of the subproblems can be efficiently solved by an iterative scheme. Simulations and in vivo experiments demonstrate the significant improvement of the proposed method compared to conventional CS-MRI algorithms, and the feasibleness on MR data compared to existing tree-based imaging algorithms.     

A simple application of compressed sensing to further accelerate partially parallel imaging

Compressed sensing (CS) and partially parallel imaging (PPI) enable fast magnetic resonance (MR) imaging by reducing the amount of k-space data required for reconstruction. Past attempts to combine these two have been limited by the incoherent sampling requirement of CS since PPI routines typically sample on a regular (coherent) grid. Here, we developed a new method, “CS+GRAPPA,” to overcome this limitation. We decomposed sets of equidistant samples into multiple random subsets. Then, we reconstructed each subset using CS and averaged the results to get a final CS k-space reconstruction. We used both a standard CS and an edge- and joint-sparsity-guided CS reconstruction. We tested these intermediate results on both synthetic and real MR phantom data and performed a human observer experiment to determine the effectiveness of decomposition and to optimize the number of subsets. We then used these CS reconstructions to calibrate the generalized autocalibrating partially parallel acquisitions (GRAPPA) complex coil weights. In vivo parallel MR brain and heart data sets were used. An objective image quality evaluation metric, Case-PDM, was used to quantify image quality. Coherent aliasing and noise artifacts were significantly reduced using two decompositions. More decompositions further reduced coherent aliasing and noise artifacts but introduced blurring. However, the blurring was effectively minimized using our new edge- and joint-sparsity-guided CS using two decompositions. Numerical results on parallel data demonstrated that the combined method greatly improved image quality as compared to standard GRAPPA, on average halving Case-PDM scores across a range of sampling rates. The proposed technique allowed the same Case-PDM scores as standard GRAPPA using about half the number of samples. We conclude that the new method augments GRAPPA by combining it with CS, allowing CS to work even when the k-space sampling pattern is equidistant.     

Adaptive k-space sampling design for edge-enhanced DCE-MRI using compressed sensing

The critical challenge in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is the trade-off between spatial and temporal resolution due to the limited availability of acquisition time. To address this, it is imperative to under-sample k-space and to develop specific reconstruction techniques. Our proposed method reconstructs high-quality images from under-sampled dynamic k-space data by proposing two main improvements; i) design of an adaptive k-space sampling lattice and ii) edge-enhanced reconstruction technique. A high-resolution data set obtained before the start of the dynamic phase is utilized. The sampling pattern is designed to adapt to the nature of k-space energy distribution obtained from the static high-resolution data. For image reconstruction, the well-known compressed sensing-based total variation (TV) minimization constrained reconstruction scheme is utilized by incorporating the gradient information obtained from the static high-resolution data. The proposed method is tested on seven real dynamic time series consisting of 2 breast data sets and 5 abdomen data sets spanning 1196 images in all. For data availability of only 10%, performance improvement is seen across various quality metrics. Average improvements in Universal Image Quality Index and Structural Similarity Index Metric of up to 28% and 24% on breast data and about 17% and 9% on abdomen data, respectively, are obtained for the proposed method as against the baseline TV reconstruction with variable density random sampling pattern.     

Two dimensional prolate spheroidal wave functions for MRI

The tradeoff between spatial and temporal resolution is often used to increase data acquisition speed for dynamic MR imaging. Reduction of the k-space sampling area, however, leads to stronger partial volume and truncation effects. A two dimensional prolate spheroidal wave function (2D-PSWF) method is developed to address these problems. Utilizing prior knowledge of a given region of interest (ROI) and the spatial resolution requirement as constraints, this method tailors the k-space sampling area with a matching 2D-PSWF filter so that optimal signal concentration and minimal truncation artifacts are achieved. The k-space sampling area is reduced because the shape and size of the sampling area match the resolution posed by the non-rectangular shape of a convex ROI. The 2D-PSWF method offers an efficient way for spatial and temporal tradeoff with minimal penalty due to truncation, and thus, it promises a wide range of applications in MRI research.     

Fast single image super-resolution using estimated low-frequency k-space data in MRI

PurposeSingle image super-resolution (SR) is highly desired in many fields but obtaining it is often technically limited in practice. The purpose of this study was to propose a simple, rapid and robust single image SR method in magnetic resonance (MR) imaging (MRI).MethodsThe idea is based on the mathematical formulation of the intrinsic link in k-space between a given (modulus) low-resolution (LR) image and the desired SR image. The method consists of two steps: 1) estimating the low-frequency k-space data of the desired SR image from a single LR image; 2) reconstructing the SR image using the estimated low-frequency and zero-filled high-frequency k-space data. The method was evaluated on digital phantom images, physical phantom MR images and real brain MR images, and compared with existing SR methods.ResultsThe proposed SR method exhibited a good robustness by reaching a clearly higher PSNR (25.77dB) and SSIM (0.991) averaged over different noise levels in comparison with existing edge-guided nonlinear interpolation (EGNI) (PSNR=23.78dB, SSIM=0.983), zero-filling (ZF) (PSNR=24.09dB, SSIM=0.985) and total variation (TV) (PSNR=24.54dB, SSIM=0.987) methods while presenting the same order of computation time as the ZF method but being much faster than the EGNI or TV method. The average PSNR or SSIM over different slice images of the proposed method (PSNR=26.33 dB or SSIM=0.955) was also higher than the EGNI (PSNR=25.07dB or SSIM=0.952), ZF (PSNR=24.97dB or SSIM=0.950) and TV (PSNR=25.70dB or SSIM=0.953) methods, demonstrating its good robustness to variation in anatomical structure of the images. Meanwhile, the proposed method always produced less ringing artifacts than the ZF method, gave a clearer image than the EGNI method, and did not exhibit any blocking effect presented in the TV method. In addition, the proposed method yielded the highest spatial consistency in the inter-slice dimension among the four methods.ConclusionsThis study proposed a fast, robust and efficient single image SR method with high spatial consistency in the inter-slice dimension for clinical MR images by estimating the low-frequency k-space data of the desired SR image from a single spatial modulus LR image.     

Phase-constrained parallel MR image reconstruction

A generalized method for phase-constrained parallel MR image reconstruction is presented that combines and extends the concepts of partial-Fourier reconstruction and parallel imaging. It provides a framework for reconstructing images employing either or both techniques and for comparing image quality achieved by varying k-space sampling schemes. The method can be used as a parallel image reconstruction with a partial-Fourier reconstruction built in. It can also be used with trajectories not readily handled by straightforward combinations of partial-Fourier and SENSE-like parallel reconstructions, including variable-density, and non-Cartesian trajectories. The phase constraint specifies a better-conditioned inverse problem compared to unconstrained parallel MR reconstruction alone. This phase-constrained parallel MRI reconstruction offers a one-step alternative to the standard combination of homodyne and SENSE reconstructions with the added benefit of flexibility of sampling trajectory. The theory of the phase-constrained approach is outlined, and its calibration requirements and limitations are discussed. Simulations, phantom experiments, and in vivo experiments are presented.     

Retrospective intra-scan motion correction

This paper analyzes the effects of intra-scan motion and demonstrates the possibility of correcting them directly in k-space with a new automatic retrospective method. The method is presented for series of 2D acquisitions with Cartesian sampling. Using a reference k-space acquisition (corrected for translations) within the series, intra-scan motion parameters are accurately estimated for each trajectory in k-space of each data set in the series resulting in pseudo-random sample positions. The images are reconstructed with a Bayesian estimator that can handle sparse arbitrary sampling in k-space and reduces intra-scan rotation artefacts to the noise level. The method has been assessed by means of a Monte Carlo study on axial brain images for different signal-to-noise ratios. The accuracy of motion estimates is better than 0.1 degrees for rotation, and 0.1 and 0.05 pixel, respectively, for translation along the read and phase directions for signal-to-noise ratios higher than 6 of the signals on each trajectory. An example of reconstruction from experimental data corrupted by head motion is also given.     

O-space with high resolution readouts outperforms radial imaging

PurposeWhile O-Space imaging is well known to accelerate image acquisition beyond traditional Cartesian sampling, its advantages compared to undersampled radial imaging, the linear trajectory most akin to O-Space imaging, have not been detailed. In addition, previous studies have focused on ultrafast imaging with very high acceleration factors and relatively low resolution. The purpose of this work is to directly compare O-Space and radial imaging in their potential to deliver highly undersampled images of high resolution and minimal artifacts, as needed for diagnostic applications. We report that the greatest advantages to O-Space imaging are observed with extended data acquisition readouts.Theory and methodsA sampling strategy that uses high resolution readouts is presented and applied to compare the potential of radial and O-Space sequences to generate high resolution images at high undersampling factors. Simulations and phantom studies were performed to investigate whether use of extended readout windows in O-Space imaging would increase k-space sampling and improve image quality, compared to radial imaging.ResultsExperimental O-Space images acquired with high resolution readouts show fewer artifacts and greater sharpness than radial imaging with equivalent scan parameters. Radial images taken with longer readouts show stronger undersampling artifacts, which can cause small or subtle image features to disappear. These features are preserved in a comparable O-Space image.ConclusionsHigh resolution O-Space imaging yields highly undersampled images of high resolution and minimal artifacts. The additional nonlinear gradient field improves image quality beyond conventional radial imaging.     

Fast multivoxel two-dimensional spectroscopic imaging at 3 T

The utility of multivoxel two-dimensional chemical shift imaging in the clinical environment will ultimately be determined by the imaging time and the metabolite peaks that can be detected. Different k-space sampling schemes can be characterized by their minimum required imaging time. The use of spiral-based readout gradients effectively reduces the minimum scan time required due to simultaneous data acquisition in three k-space dimensions (k(x), k(y) and k(f(2))). A 3-T spiral-based multivoxel two-dimensional spectroscopic imaging sequence using the PRESS excitation scheme was implemented. Good performance was demonstrated by acquiring preliminary in vivo data for applications, including brain glutamate imaging, metabolite T(2) quantification and high-spatial-resolution prostate spectroscopic imaging. All protocols were designed to acquire data within a 17-min scan time at a field strength of 3 T.