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.     

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.     

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.     

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Radial imaging techniques, such as projection-reconstruction （PR）, are used in magnetic resonance imaging （MRI） for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function （PSF）. In this paper, a shaking projection （SP） k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. ASP trajectory has the same aliasing character when using half sampling frequency （or half data） for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling recon- struction. Furthermore, this method can be applied to three-dimensional （3D） hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.     

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.     

Rapid passive MR catheter visualization for endovascular therapy using nonsymmetric truncated k-space sampling strategies

Passive catheter tracking guidance by MRI is a promising approach for endovascular therapy that may have several clinical advantages over the more frequently employed active MR approaches. However, real-time MR passive tracking is problematic because it is difficult to have an image update rate >1 Hz and preserve adequate spatial and image contrast resolution. One solution for improving real-time temporal performance is the use of nonsymmetric truncated k-space sampling strategies, which acquire only a fraction of the data in both the readout and phase-encoding directions. This article investigated these acquisition strategies in combination with using (a) multicycle projection dephaser (mcPD) gradients for background suppression and (b) the projection-onto-convex sets (POCS) algorithm to reconstruct the images. The use of mcPD gradients allowed the data sampling strategies to exploit the k-space energy structure of the catheter, and POCS allowed reconstruction of high-quality MR images that were suitable for real-time passive catheter tracking and demonstrated improved geometric representations of catheter width and tip position compared to zero filling. The use of nonsymmetric truncated k-space reduced the total acquisition time.     

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.     

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.     

选择性双向顺序压缩感知重建动态磁共振成像

压缩感知是一种新兴技术,该技术能够用远低于奈奎斯特采样频率采集的信号恢复出原始信号. 压缩感知成像方法大大提高了心脏磁共振成像的采集速度,已有的方法主要利用动态图像时间相关及心脏的周期性运动特征,如采用在时间维做傅立叶变换或求解每帧数据跟参考帧数据的差异获取稀疏数据,满足压缩感知重建的要求. 该文提出了选择性双向顺序压缩感知重建算法,利用相邻帧的差异更小的特点,获取更加稀疏的差异数据,同时利用动态图像的周期性,以目标函数积分为判据,在时间顺序和时间逆序两个方向选择效果更好的方向进行数据重建,降低图像伪影和噪声. 该选择算法,可以在不增加重建时间的情况下,选择双向顺序重建中最佳的结果. 该文对心脏磁共振图像数据进行了数据处理实验,并且跟传统压缩感知算法、参考帧差异方法及匙孔成像方法进行了比较. 结果表明：该方法无论从视觉效果还是从统计结果上,都有很大的改善.     

Real-time dynamic vocal tract imaging using an accelerated spiral GRE sequence and low rank plus sparse reconstruction

PurposeTo develop a real-time dynamic vocal tract imaging method using an accelerated spiral GRE sequence and low rank plus sparse reconstruction.MethodsSpiral k-space sampling has high data acquisition efficiency and thus is suited for real-time dynamic imaging; further acceleration can be achieved by undersampling k-space and using a model-based reconstruction. Low rank plus sparse reconstruction is a promising method with fast computation and increased robustness to global signal changes and bulk motion, as the images are decomposed into low rank and sparse terms representing different dynamic components. However, the combination with spiral scanning has not been well studied. In this study an accelerated spiral GRE sequence was developed with an optimized low rank plus sparse reconstruction and compared with L1-SPIRiT and XD-GRASP methods. The off-resonance was also corrected using a Chebyshev approximation method to reduce blurring on a frame-by-frame basis.ResultsThe low rank plus sparse reconstruction method is sensitive to the weights of the low rank and sparse terms. The optimized reconstruction showed advantages over other methods with reduced aliasing and improved SNR. With the proposed method, spatial resolution of 1.3*1.3 mm² with 150 mm field-of-view (FOV) and temporal resolution of 30 frames-per-second (fps) was achieved with good image quality. Blurring was reduced using the Chebyshev approximation method.ConclusionThis work studies low rank plus sparse reconstruction using the spiral trajectory and demonstrates a new method for dynamic vocal tract imaging which can benefit studies of speech disorders.     

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.     

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.     

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.     

Optimal k-space sampling for single point imaging of transient systems

A novel approach for sampling k-space in a pure phase encoding imaging sequence is presented using the Single Point Imaging (SPI) technique. The sequence is optimised with respect to the achievable Signal-to-Noise ratio (SNR) for a given time interval via selective sparse k-space sampling, dictated by prior knowledge of the overall object of interest's shape. This allows dynamic processes featuring short T(2)( *) NMR signal to be more readily followed, in our case the absorption of moisture by a cereal-based wafer material. Further improvements in image quality are also shown via the use of complete sampling of k-space at the start or end of the series of imaging experiments; followed by subsequent use of this data for un-sampled k-space points as opposed to zero filling.     

ANTHEM: anatomically tailored hexagonal MRI

PURPOSE: This study aimed to investigate the use of anatomically tailored hexagonal sampling for scan-time and error reduction in MRI. MATERIALS AND METHODS: Anatomically tailored hexagonal MRI (ANTHEM), a method that combines hexagonal sampling with specific symmetry in anatomical geometry, is proposed. By using hexagonal sampling, aliasing artifacts are moved to regions where, due to the nature of the anatomy, aliasing is inconsequential. This can be used to either reduce scan time while maintaining spatial resolution or reduce residual errors in speedup techniques like UNFOLD and k-t BLAST/SENSE, which undersample k-space and unwrap fold-over artifacts during reconstruction. Computer simulations as well as phantom and volunteer studies were used to validate the theory. A simplified reconstruction algorithm for hexagonally sampled and subsampled k-space data was also used. RESULTS: A reduction in sampling density of 13.4% and 25% in each hexagonally sampled dimension was achieved for spherical and conical geometries without aliasing or reduction in spatial resolution. Optimal subsampling schemes that can be utilized by UNFOLD and k-t BLAST/SENSE were derived using hexagonal subsampling, which resulted in maximal, isotropic dispersal of the aliases. In combination with UNFOLD, ANTHEM was shown to move residual aliasing artifacts to the corners of the field of view, yielding reduced artifacts in CINE reconstructions. CONCLUSIONS: ANTHEM was successful in reducing acquisition time in conventional MRI and in reducing errors in UNFOLD imaging.     

IKWI-net: A cross-domain convolutional neural network for undersampled magnetic resonance image reconstruction

Magnetic resonance imaging (MRI) is widely used to get the information of anatomical structure and physiological function with the advantages of high resolution and non-invasive scanning. But the long acquisition time limits its application. To reduce the time consumption of MRI, compressed sensing (CS) theory has been proposed to reconstruct MRI images from undersampled k-space data. But conventional CS methods mostly use iterative methods that take lots of time. Recently, deep learning methods are proposed to achieve faster reconstruction, but most of them only pay attention to a single domain, such as the image domain or k-space. To take advantage of the feature representation in different domains, we propose a cross-domain method based on deep learning, which first uses convolutional neural networks (CNNs) in the image domain, k-space and wavelet domain simultaneously. The combined order of the three domains is also first studied in this work, which has a significant effect on reconstruction. The proposed IKWI-net achieves the best performance in various combinations, which utilizes CNNs in the image domain, k-space, wavelet domain and image domain sequentially. Compared with several deep learning methods, experiments show it also achieves mean improvements of 0.91 dB in peak signal-to-noise ratio (PSNR) and 0.005 in structural similarity (SSIM).     

Edge-enhanced spatiotemporal constrained reconstruction of undersampled dynamic contrast-enhanced radial MRI

Dynamic contrast-enhanced magnetic resonance imaging (MRI) is a technique used to study and track contrast kinetics in an area of interest in the body over time. Reconstruction of images with high contrast and sharp edges from undersampled data is a challenge. While good results have been reported using a radial acquisition and a spatiotemporal constrained reconstruction (STCR) method, we propose improvements from using spatially adaptive weighting and an additional edge-based constraint. The new method uses intensity gradients from a sliding window reference image to improve the sharpness of edges in the reconstructed image. The method was tested on eight radial cardiac perfusion data sets with 24 rays and compared to the STCR method. The reconstructions showed that the new method, termed edge-enhanced spatiotemporal constrained reconstruction, was able to reconstruct images with sharper edges, and there were a 36%±13.7% increase in contrast-to-noise ratio and a 24%±11% increase in contrast near the edges when compared to STCR. The novelty of this paper is the combination of spatially adaptive weighting for spatial total variation (TV) constraint along with a gradient matching term to improve the sharpness of edges. The edge map from a reference image allows the reconstruction to trade-off between TV and edge enhancement, depending on the spatially varying weighting provided by the edge map.     

Compressive sampling photoacoustic tomography based on edge expander codes and TV regularization

A new photoacoustic （PA） signal sampling and image reconstruction method, called compressive sampling PA tomography （CSPAT）, is recently proposed to make low sampling rate and high-resolution PA tomogra- phy possible. A key problem within the CSPAT framework is the design of optic masks. We propose to use edge expander codes-based masks instead of the conventional random distribution masks, and efficient total variation （TV） regularization-based model to formulate the associated problem. The edge expander codesbased masks, corresponding to non-uniform sampling schemes, are validated by both theoretical analysis and results from computer simulations. The proposed method is expected to enhance the capability of CSPAT for reducing the number of measurements and fast data acquisition.     

An approach to real-time magnetic resonance imaging for speech production

Magnetic resonance imaging (MRI) has served as a valuable tool for studying static postures in speech production. Now, recent improvements in temporal resolution are making it possible to examine the dynamics of vocal-tract shaping during fluent speech using MRI. The present study uses spiral k-space acquisitions with a low flip-angle gradient echo pulse sequence on a conventional GE Signa 1.5-T CV/i scanner. This strategy allows for acquisition rates of 8-9 images per second and reconstruction rates of 20-24 images per second, making veridical movies of speech production now possible. Segmental durations, positions, and interarticulator timing can all be quantitatively evaluated. Data show clear real-time movements of the lips, tongue, and velum. Sample movies and data analysis strategies are presented.     

DeepcomplexMRI: Exploiting deep residual network for fast parallel MR imaging with complex convolution

This paper proposes a multi-channel image reconstruction method, named DeepcomplexMRI, to accelerate parallel MR imaging with residual complex convolutional neural network. Different from most existing works which rely on the utilization of the coil sensitivities or prior information of predefined transforms, DeepcomplexMRI takes advantage of the availability of a large number of existing multi-channel groudtruth images and uses them as target data to train the deep residual convolutional neural network offline. In particular, a complex convolutional network is proposed to take into account the correlation between the real and imaginary parts of MR images. In addition, the k-space data consistency is further enforced repeatedly in between layers of the network. The evaluations on in vivo datasets show that the proposed method has the capability to recover the desired multi-channel images. Its comparison with state-of-the-art methods also demonstrates that the proposed method can reconstruct the desired MR images more accurately.