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.     

一种结合并行成像和压缩感知的快速磁共振成像新方法

压缩感知（CS）技术和并行成像技术（主要是SENSE技术、GRAPPA技术等）都能通过减少k空间数据的采集量来加快磁共振成像速度,目前已有一些将两种方法相结合进一步加速磁共振成像速度的方法（例如CS-GRAPPA）.本文针对数据采集和重建这两方面对现有CS-GRAPPA方法进行了改进,采集方式上采用了局部等间隔采集模板以满足GRAPPA重建的要求,并对采集模板进行随机放置以满足CS重建的要求;数据重建时,根据自动校正数据估算GRAPPA算法中欠采行的重建误差,并利用误差的大小确定在CS算法中保真的程度.不同磁共振图像重建实验的结果表明：与现有方法相比,本文方法能够更好地保留原有图像细节并有效减少伪影.     

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.     

Three dimension double inversion recovery gray matter imaging using compressed sensing

The double inversion recovery (DIR) imaging technique has various applications such as black blood magnetic resonance imaging and gray/white matter imaging. Recent clinical studies show the promise of DIR for high resolution three dimensional (3D) gray matter imaging. One drawback in this case however is the long data acquisition time needed to obtain the fully sampled 3D spatial frequency domain (k-space) data. In this paper, we propose a method to solve this problem using the compressed sensing (CS) algorithm with contourlet transform. The contourlet transform is an effective sparsifying transform especially for images with smooth contours. Therefore, we applied this algorithm to undersampled DIR images and compared with a CS algorithm using wavelet transform by evaluating the reconstruction performance of each algorithm for undersampled k-space data. The results show that the proposed CS algorithm achieves a more accurate reconstruction in terms of the mean structural similarity index and root mean square error than the CS algorithm using wavelet transform.     

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.     

Improving dynamic contrast-enhanced MRI of the lung using motion-weighted sparse reconstruction: Initial experiences in patients

PurposeThe purpose of this study was to evaluate the performance of motion-weighted Golden-angle RAdial Sparse Parallel MRI (motion-weighted GRASP) for free-breathing dynamic contrast-enhanced MRI (DCE-MRI) of the lung.MethodsMotion-weighted GRASP incorporates a soft-gating motion compensation algorithm into standard GRASP reconstruction, so that motion-corrupted motion k-space (e.g., k-space acquired in inspiratory phases) contributes less to the final reconstructed images. Lung MR data from 20 patients (mean age = 57.9 ± 13.5) with known pulmonary lesions were retrospectively collected for this study. Each subject underwent a free-breathing DCE-MR scan using a fat-statured T₁-weighted stack-of-stars golden-angle radial sequence and a post-contrast breath-hold MR scan using a Cartesian volumetric-interpolated imaging sequence (BH-VIBE). Each radial dataset was reconstructed using GRASP without motion compensation and motion-weighted GRASP. All MR images were visually evaluated by two experienced radiologists blinded to reconstruction and acquisition schemes independently. In addition, the influence of motion-weighted reconstruction on dynamic contrast-enhancement patterns was also investigated.ResultsFor image quality assessment, motion-weighted GRASP received significantly higher visual scores than GRASP (P < 0.05) for overall image quality (3.68 vs. 3.39), lesion conspicuity (3.54 vs. 3.18) and overall artifact level (3.53 vs. 3.15). There was no significant difference (P > 0.05) between the breath-hold BH-VIBE and motion-weighted GRASP images. For assessment of temporal fidelity, motion-weighted GRASP maintained a good agreement with respect to GRASP.ConclusionMotion-weighted GRASP achieved better reconstruction performance in free-breathing DCE-MRI of the lung compared to standard GRASP, and it may enable improved assessment of pulmonary lesions.     

Exploiting rank deficiency and transform domain sparsity for MR image reconstruction

The reconstruction of magnetic resonance (MR) images from the partial samples of their k-space data using compressed sensing (CS)-based methods has generated a lot of interest in recent years. To reconstruct the MR images, these techniques exploit the sparsity of the image in a transform domain (wavelets, total variation, etc.). In a recent work, it has been shown that it is also possible to reconstruct MR images by exploiting their rank deficiency. In this work, it will be shown that, instead of exploiting the sparsity of the image or rank deficiency alone, better reconstruction results can be achieved by combining transform domain sparsity with rank deficiency.To reconstruct an MR image using its transform domain sparsity and its rank deficiency, this work proposes a combined l₁-norm (of the transform coefficients) and nuclear norm (of the MR image matrix) minimization problem. Since such an optimization problem has not been encountered before, this work proposes and derives a first-order algorithm to solve it.The reconstruction results show that the proposed approach yields significant improvements, in terms of both visual quality as well as the signal to noise ratio, over previous works that reconstruct MR images either by exploiting rank deficiency or by the standard CS-based technique popularly known as the ‘Sparse MRI.’     

Dual-domain cascade of U-nets for multi-channel magnetic resonance image reconstruction

The U-net is a deep-learning network model that has been used to solve a number of inverse problems. In this work, the concatenation of two-element U-nets, termed the W-net, operating in k-space (K) and image (I) domains, were evaluated for multi-channel magnetic resonance (MR) image reconstruction. The two-element network combinations were evaluated for the four possible image-k-space domain configurations: a) W-net II, b) W-net KK, c) W-net IK, and d) W-net KI. Selected four element (WW-nets) and six element (WWW-nets) networks were also examined. Two configurations of each network were compared: 1) each coil channel was processed independently, and 2) all channels were processed simultaneously. One hundred and eleven volumetric, T1-weighted, 12-channel coil k-space datasets were used in the experiments. Normalized root mean squared error, peak signal-to-noise ratio and visual information fidelity were used to assess the reconstructed images against the fully sampled reference images. Our results indicated that networks that operate solely in the image domain were better when independently processing individual channels of multi-channel data. Dual-domain methods were better when simultaneously reconstructing all channels of multi-channel data. In addition, the best cascade of U-nets performed better (p < 0.01) than the previously published, state-of-the-art Deep Cascade and Hybrid Cascade models in three out of four experiments.     

Undersampled MRI reconstruction with patch-based directional wavelets

Compressed sensing has shown great potential in reducing data acquisition time in magnetic resonance imaging (MRI). In traditional compressed sensing MRI methods, an image is reconstructed by enforcing its sparse representation with respect to a preconstructed basis or dictionary. In this paper, patch-based directional wavelets are proposed to reconstruct images from undersampled k-space data. A parameter of patch-based directional wavelets, indicating the geometric direction of each patch, is trained from the reconstructed image using conventional compressed sensing MRI methods and incorporated into the sparsifying transform to provide the sparse representation for the image to be reconstructed. A reconstruction formulation is proposed and solved via an efficient alternating direction algorithm. Simulation results on phantom and in vivo data indicate that the proposed method outperforms conventional compressed sensing MRI methods in preserving the edges and suppressing the noise. Besides, the proposed method is not sensitive to the initial image when training directions.     

Accelerated free-breathing 3D whole-heart magnetic resonance angiography with a radial phyllotaxis trajectory,compressed sensing,and curvelet transform

PurposeTo develop and validate an accelerated free-breathing 3D whole-heart magnetic resonance angiography (MRA) technique using a radial k-space trajectory with compressed sensing and curvelet transform.MethodA 3D radial phyllotaxis trajectory was implemented to traverse the centerline of k-space immediately before the segmented whole-heart MRA data acquisition at each cardiac cycle. The k-space centerlines were used to correct the respiratory-induced heart motion in the acquired MRA data. The corrected MRA data were then reconstructed by a novel compressed sensing algorithm using curvelets as the sparsifying domain. The proposed 3D whole-heart MRA technique (radial CS curvelet) was then prospectively validated against compressed sensing with a conventional wavelet transform (radial CS wavelet) and a standard Cartesian acquisition in terms of scan time and border sharpness.ResultsFifteen patients (females 10, median age 34-year-old) underwent 3D whole-heart MRA imaging using a standard Cartesian trajectory and our proposed radial phyllotaxis trajectory. Scan time for radial phyllotaxis was significantly shorter than Cartesian (4.88 ± 0.86 min. vs. 6.84 ± 1.79 min., P-value = 0.004). Radial CS curvelet border sharpness was slightly lower than Cartesian and, for the majority of vessels, was significantly better than radial CS wavelet (P-value < 0.050).ConclusionThe proposed technique of 3D whole-heart MRA acquisition with a radial CS curvelet has a shorter scan time and slightly lower vessel sharpness compared to the Cartesian acquisition with radial profile ordering, and has slightly better sharpness than radial CS wavelet. Future work on this technique includes additional clinical trials and extending this technique to 3D cine imaging.     

Accelerated electron paramagnetic resonance imaging using partial Fourier compressed sensing reconstruction

PurposeElectron paramagnetic resonance (EPR) imaging has evolved as a promising tool to provide non-invasive assessment of tissue oxygenation levels. Due to the extremely short T₂ relaxation time of electrons, single point imaging (SPI) is used in EPRI, limiting achievable spatial and temporal resolution. This presents a problem when attempting to measure changes in hypoxic state. In order to capture oxygen variation in hypoxic tissues and localize cycling hypoxia regions, an accelerated EPRI imaging method with minimal loss of information is needed.MethodsWe present an image acceleration technique, partial Fourier compressed sensing (PFCS), that combines compressed sensing (CS) and partial Fourier reconstruction. PFCS augments the original CS equation using conjugate symmetry information for missing measurements. To further improve image quality in order to reconstruct low-resolution EPRI images, a projection onto convex sets (POCS)-based phase map and a spherical-sampling mask are used in the reconstruction process. The PFCS technique was used in phantoms and in vivo SCC7 tumor mice to evaluate image quality and accuracy in estimating O₂ concentration.ResultsIn both phantom and in vivo experiments, PFCS demonstrated the ability to reconstruct images more accurately with at least a 4-fold acceleration compared to traditional CS. Meanwhile, PFCS is able to better preserve the distinct spatial pattern in a phantom with a spatial resolution of 0.6 mm. On phantoms containing Oxo63 solution with different oxygen concentrations, PFCS reconstructed linewidth maps that were discriminative of different O₂ concentrations. Moreover, PFCS reconstruction of partially sampled data provided a better discrimination of hypoxic and oxygenated regions in a leg tumor compared to traditional CS reconstructed images.ConclusionsEPR images with an acceleration factor of four are feasible using PFCS with reasonable assessment of tissue oxygenation. The technique can greatly enhance EPR applications and improve our understanding cycling hypoxia. Moreover this technique can be easily extended to various MRI applications.     

Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization

Reducing scanning time is significantly important for MRI. Compressed sensing has shown promising results by undersampling the k-space data to speed up imaging. Sparsity of an image plays an important role in compressed sensing MRI to reduce the image artifacts. Recently, the method of patch-based directional wavelets (PBDW) which trains geometric directions from undersampled data has been proposed. It has better performance in preserving image edges than conventional sparsifying transforms. However, obvious artifacts are presented in the smooth region when the data are highly undersampled. In addition, the original PBDW-based method does not hold obvious improvement for radial and fully 2D random sampling patterns. In this paper, the PBDW-based MRI reconstruction is improved from two aspects: 1) An efficient non-convex minimization algorithm is modified to enhance image quality; 2) PBDW are extended into shift-invariant discrete wavelet domain to enhance the ability of transform on sparsifying piecewise smooth image features. Numerical simulation results on vivo magnetic resonance images demonstrate that the proposed method outperforms the original PBDW in terms of removing artifacts and preserving edges.     

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).     

Triple-D network for efficient undersampled magnetic resonance images reconstruction

Compressed sensing (CS) theory can help accelerate magnetic resonance imaging (MRI) by sampling partial k-space measurements. However, conventional optimization-based CS-MRI methods are often time-consuming and are based on fixed transform or shallow image dictionaries, which limits modeling capabilities. Recently, deep learning models have been used to solve the CS-MRI problem. However, recent researches have focused on modeling in image domain, and the potential of k-space modeling capability has not been utilized seriously. In this paper, we propose a deep model called Dual Domain Dense network (Triple-D network), which consisted of some k-space and image domain sub-network. These sub-networks are connected with dense connections, which can utilize feature maps at different levels to enhance performance. To further promote model capabilities, we use two strategies: multi-supervision strategies, which can avoid loss of supervision information; channel-wise attention layer (CA layer), which can adaptively adjust the weight of the feature map. Experimental results show that the proposed Triple-D network provides promising performance in CS-MRI, and it can effectively work on different sampling trajectories and noisy settings.     

Joint Reconstruction of Multi-contrast Images and Multi-channel Coil Sensitivities

Magnetic resonance imaging (MRI) has an important feature that it provides multiple images with different contrasts for complementary diagnostic information. However, a large amount of data is needed for multi-contrast images depiction, and thus, the scan is time-consuming. Many methods based on parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) are applied to accelerate multi-contrast MR imaging. Nevertheless, the image reconstructed by sophisticated pMRI methods contains residual aliasing artifact that degrades the quality of the image when the acceleration factor is high. Other methods based on CS always suffer the regularization parameter-selecting problem. To address these issues, a new method is presented for joint multi-contrast image reconstruction and coil sensitivity estimation. The coil sensitivities can be shared during the reconstruction due to the identity of coil sensitivity profiles of different contrast images for imaging stationary tissues. The proposed method uses the coil sensitivities as sharable information during the reconstruction to improve the reconstruction quality. As a result, the residual aliasing artifact can be effectively removed in the reconstructed multi-contrast images even if the acceleration factor is high. Besides, as there is no regularization term in the proposed method, the troublesome regularization parameter selection in the CS can also be avoided. Results from multi-contrast in vivo experiments demonstrated that multi-contrast images can be jointly reconstructed by the proposed method with effective removal of the residual aliasing artifact at a high acceleration factor.     

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.     

Cardiac magnetic resonance imaging using radial k-space sampling and self-calibrated partial parallel reconstruction

Radial sampling has been demonstrated to be potentially useful in cardiac magnetic resonance imaging because it is less susceptible to motion than Cartesian sampling. Nevertheless, its capability of imaging acceleration remains limited by undersampling-induced streaking artifacts. In this study, a self-calibrated reconstruction method was developed to suppress streaking artifacts for highly accelerated parallel radial acquisitions in cardiac magnetic resonance imaging. Two- (2D) and three-dimensional (3D) radial k-space data were collected from a phantom and healthy volunteers. Images reconstructed using the proposed method and the conventional regridding method were compared based on statistical analysis on a four-point scale imaging scoring. It was demonstrated that the proposed method can effectively remove undersampling streaking artifacts and significantly improve image quality (P<.05). With the use of the proposed method, image score (1–4, 1=poor, 2=good, 3=very good, 4=excellent) was improved from 2.14 to 3.34 with the use of an undersampling factor of 4 and from 1.09 to 2.5 with the use of an undersampling factor of 8. Our study demonstrates that the proposed reconstruction method is effective for highly accelerated cardiac imaging applications using parallel radial acquisitions without calibration data.     

Compressed sensing MR image reconstruction using a motion-compensated reference

Compressed sensing (CS)-based methods have been proposed for image reconstruction from undersampled magnetic resonance data. Recently, CS-based schemes using reference images have also been proposed to further reduce the sampling requirement. In this study, we propose a new reference-constrained CS reconstruction method that accounts for the misalignment between the reference and the target image to be reconstructed. The proposed method uses a new image model that represents the target image as a linear combination of a motion-dependent reference image and a sparse difference image. We then use an efficient iterative algorithm to jointly estimate the motion parameters and the difference image from sparsely sampled data. Simulation results from a numerical phantom data set and an in vivo data set show that the proposed method can accurately compensate the motion effects between the reference and the target images and improve reconstruction quality. The proposed method should prove useful for several applications such as interventional imaging, longitudinal imaging studies and dynamic contrast-enhanced imaging.     

Multiphase Segmented K-Space Velocity Mapping in Pulsatile Flow Waveforms

The aim of the present study was to obtain the precision of flow measurement in breath-hold segmented k-space flow sequences. The results are based on studies of pulsatile flow in a phantom tube. The ultimate purpose is to use these sequences to measure coronary flow. In abdominal and cardiothoracic magnetic resonance imaging the image quality is degraded due to respiratory motion. In the segmented k-space acquisition method, one obtains many phase-encoding steps or views per cardiac phase. This shortens imaging time in the order of phase-encoding lines and makes it possible to image in a single breath-hold, thereby eliminating respiratory artefacts and improving edge detection. With breath-hold multiframe cine flow images it is possible to evaluate flow in all abdominal and cardiothoracic areas, including the coronary arteries. Our study shows that velocity curves shift in time when the number of k-space k_y-lines per segment (LPS) are varied; this shift is linear as a function of LPS. The mean velocity V_mean in the center of mass of the pulsatile peak is constant (V_mean = 40.1 ± 2.9 cm/s) and time t = −10.1 × LPS + 268 (r = 0.993, p < 0.0001). Correlation between theoretical and experimental flow curves is also linear as a function of LPS: C = −0.977 1 LPS (r = 0.987, p < 0.0001). It is concluded that velocity curves move with LPS and are smoothed when the breath-hold velocity mapping is used. The more LPS is gathered the more inaccurate results are. LPS 7 or more cannot be considered clinically relevant.     

Singular Value Decomposition Using Jacobi Algorithm in pMRI and CS

Parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) have been recently used to accelerate data acquisition process in MRI. Matrix inversion (for rectangular matrices) is required to reconstruct images from the acquired under-sampled data in various pMRI algorithms (e.g., SENSE, GRAPPA) and CS. Singular value decomposition (SVD) provides a mechanism to accurately estimate pseudo-inverse of a rectangular matrix. This work proposes the use of Jacobi SVD algorithm to reconstruct MR images from the acquired under-sampled data both in pMRI and in CS. The use of Jacobi SVD algorithm is proposed in advance MRI reconstruction algorithms, including SENSE, GRAPPA, and low-rank matrix estimation in L + S model for matrix inversion and estimation of singular values. Experiments are performed on 1.5T human head MRI data and 3T cardiac perfusion MRI data for different acceleration factors. The reconstructed images are analyzed using artifact power and central line profiles. The results show that the Jacobi SVD algorithm successfully reconstructs the images in SENSE, GRAPPA, and L + S algorithms. The benefit of using Jacobi SVD algorithm for MRI image reconstruction is its suitability for parallel computation on GPUs, which may be a great help in reducing the image reconstruction time.