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.     

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.     

De-aliasing for signal restoration in Propeller MR imaging

PurposeObjects falling outside of the true elliptical field-of-view (FOV) in Propeller imaging show unique aliasing artifacts. This study proposes a de-aliasing approach to restore the signal intensities in Propeller images without extra data acquisition.Materials and methodsComputer simulation was performed on the Shepp-Logan head phantom deliberately placed obliquely to examine the signal aliasing. In addition, phantom and human imaging experiments were performed using Propeller imaging with various readouts on a 3.0 Tesla MR scanner. De-aliasing using the proposed method was then performed, with the first low-resolution single-blade image used to find out the aliasing patterns in all the single-blade images, followed by standard Propeller reconstruction. The Propeller images without and with de-aliasing were compared.ResultsComputer simulations showed signal loss at the image corners along with aliasing artifacts distributed along directions corresponding to the rotational blades, consistent with clinical observations. The proposed de-aliasing operation successfully restored the correct images in both phantom and human experiments.ConclusionThe de-aliasing operation is an effective adjunct to Propeller MR image reconstruction for retrospective restoration of aliased signals.     

A multi-scale residual network for accelerated radial MR parameter mapping

A deep learning MR parameter mapping framework which combines accelerated radial data acquisition with a multi-scale residual network (MS-ResNet) for image reconstruction is proposed. The proposed supervised learning strategy uses input image patches from multi-contrast images with radial undersampling artifacts and target image patches from artifact-free multi-contrast images. Subspace filtering is used during pre-processing to denoise input patches. For each anatomy and relaxation parameter, an individual network is trained. in vivo T₁ mapping results are obtained on brain and abdomen datasets and in vivo T₂ mapping results are obtained on brain and knee datasets. Quantitative results for the T₂ mapping of the knee show that MS-ResNet trained using either fully sampled or undersampled data outperforms conventional model-based compressed sensing methods. This is significant because obtaining fully sampled training data is not possible in many applications. in vivo brain and abdomen results for T₁ mapping and in vivo brain results for T₂ mapping demonstrate that MS-ResNet yields contrast-weighted images and parameter maps that are comparable to those achieved by model-based iterative methods while offering two orders of magnitude reduction in reconstruction times. The proposed approach enables recovery of high-quality contrast-weighted images and parameter maps from highly accelerated radial data acquisitions. The rapid image reconstructions enabled by the proposed approach makes it a good candidate for routine clinical use.     

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.     

Smoothly Clipped Absolute Deviation (SCAD) regularization for compressed sensing MRI Using an augmented Lagrangian scheme

PurposeCompressed sensing (CS) provides a promising framework for MR image reconstruction from highly undersampled data, thus reducing data acquisition time. In this context, sparsity-promoting regularization techniques exploit the prior knowledge that MR images are sparse or compressible in a given transform domain. In this work, a new regularization technique was introduced by iterative linearization of the non-convex smoothly clipped absolute deviation (SCAD) norm with the aim of reducing the sampling rate even lower than it is required by the conventional l₁ norm while approaching an l₀ norm.Materials and MethodsThe CS-MR image reconstruction was formulated as an equality-constrained optimization problem using a variable splitting technique and solved using an augmented Lagrangian (AL) method developed to accelerate the optimization of constrained problems. The performance of the resulting SCAD-based algorithm was evaluated for discrete gradients and wavelet sparsifying transforms and compared with its l₁-based counterpart using phantom and clinical studies. The k-spaces of the datasets were retrospectively undersampled using different sampling trajectories. In the AL framework, the CS-MRI problem was decomposed into two simpler sub-problems, wherein the linearization of the SCAD norm resulted in an adaptively weighted soft thresholding rule with a sparsity enhancing effect.ResultsIt was demonstrated that the proposed regularization technique adaptively assigns lower weights on the thresholding of gradient fields and wavelet coefficients, and as such, is more efficient in reducing aliasing artifacts arising from k-space undersampling, when compared to its l₁-based counterpart.ConclusionThe SCAD regularization improves the performance of l₁-based regularization technique, especially at reduced sampling rates, and thus might be a good candidate for some applications in CS-MRI.     

基于同伦l0范数最小化重建的三维动态磁共振成像

高欠采倍数的动态磁共振图像重建具有重要意义,是同时实现高时间分辨率和高空间分辨率动态对比度增强成像的重要环节.本研究提出一种结合黄金角变密度螺旋采样、并行成像和基于同伦l₀范数最小化的压缩感知的图像重建的三维动态磁共振成像方法.黄金角变密度螺旋采样轨迹被用来连续获取k空间数据,具有数据采集效率高、对运动不敏感等优点.在重建算法中,将多线圈稀疏约束应用于时间总变分域,使用基于l₀范数最小化的非线性重建算法代替传统的l₁范数最小化算法,进一步提高了欠采样率.仿真实验和在体实验表明本文所提的方法在保持图像质量的同时,也可以实现较高的空间分辨率和时间分辨率,初步验证了基于同伦l₀范数最小化重建在三维动态磁共振成像上的优势和临床价值.     

Accelerating quantitative MR imaging with the incorporation of B1 compensation using deep learning

Quantitative magnetic resonance imaging (MRI) attracts attention due to its support to quantitative image analysis and data driven medicine. However, the application of quantitative MRI is severely limited by the long data acquisition time required by repetitive image acquisition and measurement of field map. Inspired by recent development of artificial intelligence, we propose a deep learning strategy to accelerate the acquisition of quantitative MRI, where every quantitative T₁ map is derived from two highly undersampled variable-contrast images with radiofrequency field inhomogeneity automatically compensated. In a multi-step framework, variable-contrast images are first jointly reconstructed from incoherently undersampled images using convolutional neural networks; then T₁ map and B₁ map are predicted from reconstructed images employing deep learning. Thus, the acceleration includes undersampling in every input image, a reduction in the number of variable contrast images, as well as a waiver of B₁ map measurement. The strategy is validated in T₁ mapping of cartilage. Acquired with a consistent imaging protocol, 1224 image sets from 51 subjects are used for the training of the prediction models, and 288 image sets from 12 subjects are used for testing. High degree of acceleration is achieved with image fidelity well maintained. The proposed method can be broadly applied to quantify other tissue properties (e.g. T₂, T_1ρ) as well.     

Feasibility of free-breathing T1-weighted 3D radial VIBE for fetal MRI in various anomalies

Rationale and objectivesIn magnetic resonance (MR) fetal imaging, the image quality acquired by the traditional Cartesian-sampled breath-hold T1-weighted (T1W) sequence may be degraded by motion artifacts arising from both mother and fetus. The radial VIBE sequence is reported to be a viable alternative to conventional Cartesian acquisition for both pediatric and adult MR, yielding better image quality. This study evaluated the role of radial VIBE in fetal MR imaging and compared its image quality and motion artifacts with those of the Cartesian T1W sequence.Materials and methodsWe included 246 pregnant women with 50 lesions on 1.5-T MR imaging. Image quality and lesion conspicuity were evaluated by two radiologists, blinded to the acquisition schemes used, using a five-point scale, where a higher score indicated a better trajectory method. Mixed-model analysis of variance and interobserver variability assessment were performed.ResultsThe radial VIBE sequence showed a significantly better performance than conventional T1W imaging in the head and neck, fetal body, and placenta region: 3.92 ± 0.88 vs 3 ± 0.74, p < 0.001, 3.8 ± 0.94 vs 3.15 ± 0.87, p < 0.001, and 4.17 ± 0.63 vs 3.12 ± 0.72, p < 0.001, respectively. Additionally, fewer motion artifacts were observed in all regions with the radial VIBE sequence (p < 0.01). Of 50 lesions, 49 presented better lesion conspicuity on radial VIBE images than on T1W images (4.34 ± 0.91 vs 3.48 ± 1.46, p < 0.001).ConclusionFor fetal imaging, the radial VIBE sequences yielded better image quality and lesion conspicuity, with fewer motion artifacts, than conventional breath-hold Cartesian-sampled T1W sequences.     

Autocalibrated parallel imaging reconstruction with sampling pattern optimization for GRASE: APIR4GRASE

PurposeTo reduce artifacts and scan time of GRASE imaging by selecting an optimal sampling pattern and jointly reconstructing gradient echo and spin echo images.MethodsWe jointly reconstruct images for the different echo types by considering these as additional virtual coil channels in the novel Autocalibrated Parallel Imaging Reconstruction with Sampling Pattern Optimization for GRASE (APIR4GRASE) method. Besides image reconstruction, we identify optimal sampling patterns for the acquisition. The selected optimal patterns were validated on phantom and in-vivo acquisitions. Comparison to the conventional GRASE without acceleration, and to the GRAPPA reconstruction with a single echo type was also performed.ResultsUsing identified optimal sampling patterns, APIR4GRASE eliminated modulation artifacts in both phantom and in-vivo experiments; mean square error (MSE) was reduced by 78% and 94%, respectively, compared to the conventional GRASE with similar scan time. Both artifacts and g-factor were reduced compared to the GRAPPA reconstruction with a single echo type.ConclusionAPIR4GRASE substantially improves the speed and quality of GRASE imaging over the state-of-the-art, and is able to reconstruct both spin echo and gradient echo images.     

Highly undersampled supraaortic MRA at 3.0 T: initial results with parallel imaging in two directions using a 16-channel neurovascular coil and parallel imaging factors up to 16

PurposeTo present the feasibility of highly undersampled contrast-enhanced MRA (CE-MRA) of the supraaortic arteries with a 16-channel neurovascular coil at 3.0 T using parallel imaging in two directions with parallel imaging factors (PIF) up to 16.Materials and MethodsInstitutional review board approval and informed consent were obtained. In a prospective study, MRA protocols including PIF of 1, 2, 4, 9 and 16 yielding a spatial resolution from 0.81×0.81×1.0 mm³ to 0.46×.46×0.98 mm³ were acquired. In 32 examinations, image quality and vascular segments were rated independently by two radiologists. SNR estimations were performed for all MRA protocols.ResultsThe use of high PIF allowed to shorten acquisition time from 2:09 min down to 1:13 min and to increase the anatomic coverage while maintaining or even increasing spatial resolution down to 0.46×0.46×0.98 mm³. The larger anatomic coverage that was achieved with the use of high PIF allowed for visualization of vascular structures that were not covered by the standard protocols. Despite the resulting lower SNR using high PIF, image quality was constantly rated to be adequate for diagnosis or better in all cases.ConclusionThe use of high PIF yielded diagnostic image quality and allowed to increase the anatomic coverage while maintaining or even improving spatial resolution and shortening the acquisition time.     

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.     

Wavelet-based edge correlation incorporated iterative reconstruction for undersampled MRI

Undersampling k-space is an effective way to decrease acquisition time for MRI. However, aliasing artifacts introduced by undersampling may blur the edges of magnetic resonance images, which often contain important information for clinical diagnosis. Moreover, k-space data is often contaminated by the noise signals of unknown intensity. To better preserve the edge features while suppressing the aliasing artifacts and noises, we present a new wavelet-based algorithm for undersampled MRI reconstruction. The algorithm solves the image reconstruction as a standard optimization problem including a ?₂ data fidelity term and ?₁ sparsity regularization term. Rather than manually setting the regularization parameter for the ?₁ term, which is directly related to the threshold, an automatic estimated threshold adaptive to noise intensity is introduced in our proposed algorithm. In addition, a prior matrix based on edge correlation in wavelet domain is incorporated into the regularization term. Compared with nonlinear conjugate gradient descent algorithm, iterative shrinkage/thresholding algorithm, fast iterative soft-thresholding algorithm and the iterative thresholding algorithm using exponentially decreasing threshold, the proposed algorithm yields reconstructions with better edge recovery and noise suppression.     

Incorporating prior knowledge via volumetric deep residual network to optimize the reconstruction of sparsely sampled MRI

For sparse sampling that accelerates magnetic resonance (MR) image acquisition, non-linear reconstruction algorithms have been developed, which incorporated patient specific a prior information. More generic a prior information could be acquired via deep learning and utilized for image reconstruction. In this study, we developed a volumetric hierarchical deep residual convolutional neural network, referred to as T-Net, to provide a data-driven end-to-end mapping from sparsely sampled MR images to fully sampled MR images, where cartilage MR images were acquired using an Ultra-short TE sequence and retrospectively undersampled using pseudo-random Cartesian and radial acquisition schemes. The network had a hierarchical architecture that promoted the sparsity of feature maps and increased the receptive field, which were valuable for signal synthesis and artifact suppression. Relatively dense local connections and global shortcuts were established to facilitate residual learning and compensate for details lost in hierarchical processing. Additionally, volumetric processing was adopted to fully exploit spatial continuity in three-dimensional space. Data consistency was further enforced. The network was trained with 336 three-dimensional images (each consisting of 32 slices) and tested by 24 images. The incorporation of a priori information acquired via deep learning facilitated high acceleration factors (as high as 8) while maintaining high image fidelity (quantitatively evaluated using the structural similarity index measurement). The proposed T-Net had an improved performance as compared to several state-of-the-art networks.     

Free-breathing dynamic contrast-enhanced magnetic resonance of interstitial lung fibrosis

PurposeComputed tomography (CT) imaging is the standard to assess interstitial lung disease. Magnetic resonance (MR) is potentially advantageous due to superior tissue characterization and better assessment of blood flow dynamics. This study aimed to evaluate idiopathic pulmonary fibrosis (IPF) using prototype 4D Stack of Stars GRE (StarVIBE) MR and compare it to CT.MethodThis IRB-approved prospective study included 13 patients [5F:8M; average age 66 ± 8.1 years] with pulmonary fibrosis, and 12 healthy controls [3F:9M; average age 55 ± 3.6 years]. MR of the chest included noncontrast steady-state free precession imaging (SSFP) and free-breathing 4D StarVIBE sequence with intravenous contrast administration up to 160 s. The images were assessed for quality and artifacts. The image resolution was evaluated based on the visibility of the smallest bronchi, vessels, lymph nodes, and pleural fissures. Independent assessment of reticulation, ground-glass opacity, and traction bronchiectasis was performed and compared to CT.ResultsThe StarVIBE images had fewer artifacts and higher spatial resolution. The findings associated with IPF were significantly better seen with StarVIBE, with superior CT correlation.ConclusionContrast-enhanced free-breathing StarVIBE MR can generate high quality images with good correlation to CT in patients with IPF, and with high spatial and temporal resolution to generate rapid sequential dynamic images.     

Deep learning for radial SMS myocardial perfusion reconstruction using the 3D residual booster U-net

PurposeTo develop an end-to-end deep learning solution for quickly reconstructing radial simultaneous multi-slice (SMS) myocardial perfusion datasets with comparable quality to the pixel tracking spatiotemporal constrained reconstruction (PT-STCR) method.MethodsDynamic contrast enhanced (DCE) radial SMS myocardial perfusion data were obtained from 20 subjects who were scanned at rest and/or stress with or without ECG gating using a saturation recovery radial CAIPI turboFLASH sequence. Input to the networks consisted of complex coil combined images reconstructed using the inverse Fourier transform of undersampled radial SMS k-space data. Ground truth images were reconstructed using the PT-STCR pipeline. The performance of the residual booster 3D U-Net was tested by comparing it to state-of-the-art network architectures including MoDL, CRNN-MRI, and other U-Net variants.ResultsResults demonstrate significant improvements in speed requiring approximately 8 seconds to reconstruct one radial SMS dataset which is approximately 200 times faster than the PT-STCR method. Images reconstructed with the residual booster 3D U-Net retain quality of ground truth PT-STCR images (0.963 SSIM/40.238 PSNR/0.147 NRMSE). The residual booster 3D U-Net has superior performance compared to existing network architectures in terms of image quality, temporal dynamics, and reconstruction time.ConclusionResidual and booster learning combined with the 3D U-Net architecture was shown to be an effective network for reconstructing high-quality images from undersampled radial SMS datasets while bypassing the reconstruction time of the PT-STCR method.     

Time-resolved contrast-enhanced coronary magnetic resonance angiography with highly constrained projection reconstruction

Contrast-enhanced magnetic resonance angiography (MRA) is a promising technique for coronary artery imaging. The blood signal changes during the contrast injection will result in image artifacts, blurring and relatively low signal-to-noise ratio, when the k-space segments from different cardiac cycles are combined to reconstruct the final image as “time averaged.” Thus, it is important to acquire data during maximal blood signal enhancement for first-pass, contrast-enhanced MRA, and relatively high temporal resolution is required. This work demonstrated the feasibility of highly constrained backprojection reconstruction for time-resolved, contrast-enhanced coronary MRA. With this method, the temporal resolution can be increased. In addition, coronary artery images around blood signal enhancement peak have significantly improved contrast-to-noise ratio and suppressed artifacts compared to the composite images which were collected during a much longer acquisition time during substantial blood signal changes.     

CS-MRI 中评价随机欠采样矩阵的新方法

在压缩感知-磁共振成像(CS-MRI)中,随机欠采样矩阵与重建图像质量密切相关．而选取随机欠采样矩阵一般是通过计算点扩散函数(PSF),以可能产生的伪影的最大值为评价参数,评估欠采样对图像重建的影响,然而最大值只反应了伪影的最坏情况．该文引入了两种新的统计学评价参数平均值(MV)和标准差(SD),其中平均值评估了伪影的平均大小,标准差可以反映伪影的波动情况．该文分别使用这3种参数对小鼠和人体脑部MRI数据以不同的采样比率进行CS图像重建,实验结果表明,当采样比率不低于4倍稀疏度时,使用平均值获得了质量更优的重建图像．因此,通过稀疏度先验知识指导合理选取采样比率,并以平均值为评价参数选取随机欠采样矩阵,能够获得更优的CS-MRI重建图像．
     

Rapid 3D whole-heart cine imaging using golden ratio stack of spirals

Three-dimensional cine imaging provides a wealth of information about cardiac anatomy and function, but its use in the clinical environment is limited because data acquisition is very time consuming. In this work, a free-breathing 3D whole-heart cine imaging framework was developed using a time-efficient stack of spirals trajectory and accelerated reconstruction. Two suitable view ordering methods are considered with different spacing between k-space readouts in the partition dimension: uniform and tiny golden ratio based. A simulation study suggested the latter did not present any benefits in terms of similarity to the true image. The proposed method was subsequently tested on 10 prospective subjects and compared with conventional multi-slice breath-hold imaging. Image quality was evaluated using objective and subjective scores and ventricular measurements were compared to assess clinical accuracy. Image quality was lower in the proposed technique than in breath-hold images but good agreement was found in clinically relevant ventricular measurements. In addition, the proposed method was fast to acquire, required minimal planning and provided full anatomical coverage with isotropic resolution.     

Spiral demystified

Spiral acquisition schemes offer unique advantages such as flow compensation, efficient k-space sampling and robustness against motion that make this option a viable choice among other non-Cartesian sampling schemes. For this reason, the main applications of spiral imaging lie in dynamic magnetic resonance imaging such as cardiac imaging and functional brain imaging. However, these advantages are counterbalanced by practical difficulties that render spiral imaging quite challenging. Firstly, the design of gradient waveforms and its hardware requires specific attention. Secondly, the reconstruction of such data is no longer straightforward because k-space samples are no longer aligned on a Cartesian grid. Thirdly, to take advantage of parallel imaging techniques, the common generalized autocalibrating partially parallel acquisitions (GRAPPA) or sensitivity encoding (SENSE) algorithms need to be extended. Finally, and most notably, spiral images are prone to particular artifacts such as blurring due to gradient deviations and off-resonance effects caused by B₀ inhomogeneity and concomitant gradient fields. In this article, various difficulties that spiral imaging brings along, and the solutions, which have been developed and proposed in literature, will be reviewed in detail.