Undersampled Images Research Articles

Deep Learning-Based MRI in Diagnosis of Fracture of Tibial Plateau Combined with Meniscus Injury

This study aimed to explore the application value of magnetic resonance imaging (MRI) images based on deep learning algorithms in the diagnosis of tibial plateau fractures combined with meniscus injuries. The original MRI image was input into the deep learning convolutional neural network (CNN), and the knee joint undersampled and fully sampled MRI image data were used for training to obtain a neural network model that can effectively remove the noise and blur of the undersampled image. Then, the image was reconstructed by the Regridding model to obtain an image with less noise and clearer structure. At the same time, all subjects underwent knee MRI examinations, and algorithms were used to analyze the sensitivity, specificity, and accuracy of their images. It was found that of 160 menisci from 80 cases of tibial plateau fractures, 64 were normal meniscus and 88 were injured menisci. The sensitivity, specificity, and accuracy of optimized MRI in diagnosing fracture of tibial plateau combined with meniscus injury were 96.9%, 93.2%, and 95.3%, respectively. In conclusion, the restored MRI images have high sensitivity in the diagnosis of meniscus injury and high consistency with the intraoperative results. It suggests that the optimized MRI image is effective in the diagnosis of meniscus injury.

Prior image-guided cone-beam computed tomography augmentation from under-sampled projections using a convolutional neural network.

Acquiring sparse-view cone-beam computed tomography (CBCT) is an effective way to reduce the imaging dose. However, images reconstructed by the conventional filtered back-projection method suffer from severe streak artifacts due to the projection under-sampling. Existing deep learning models have demonstrated feasibilities in restoring volumetric structures from the highly under-sampled images. However, because of the inter-patient variabilities, they failed to restore the patient-specific details with the common restoring pattern learned from the group data. Although the patient-specific models have been developed by training models using the intra-patient data and have shown effectiveness in restoring the patient-specific details, the models have to be retrained to be exclusive for each patient. It is highly desirable to develop a generalized model that can utilize the patient-specific information for the under-sampled image augmentation. In this study, we proposed a merging-encoder convolutional neural network (MeCNN) to realize the prior image-guided under-sampled CBCT augmentation. Instead of learning the patient-specific structures, the proposed model learns a generalized pattern of utilizing the patient-specific information in the prior images to facilitate the under-sampled image enhancement. Specifically, the MeCNN consists of a merging-encoder and a decoder. The merging-encoder extracts image features from both the prior CT images and the under-sampled CBCT images, and merges the features at multi-scale levels via deep convolutions. The merged features are then connected to the decoders via shortcuts to yield high-quality CBCT images. The proposed model was tested on both the simulated CBCTs and the clinical CBCTs. The predicted CBCT images were evaluated qualitatively and quantitatively in terms of image quality and tumor localization accuracy. Mann-Whitney U test was conducted for the statistical analysis. P<0.05 was considered statistically significant. The proposed model yields CT-like high-quality CBCT images from only 36 half-fan projections. Compared to other methods, CBCT images augmented by the proposed model have significantly lower intensity errors, significantly higher peak signal-to-noise ratio, and significantly higher structural similarity with respect to the ground truth images. Besides, the proposed method significantly reduced the 3D distance of the CBCT-based tumor localization errors. In addition, the CBCT augmentation is nearly real-time. With the prior-image guidance, the proposed method is effective in reconstructing high-quality CBCT images from the highly under-sampled projections, considerably reducing the imaging dose and improving the clinical utility of the CBCT.

Prior ensemble learning : Theory and application to MR image priors.

Compressed sensing (CS) reduces the measurement time of magnetic resonance (MR) imaging, where the use of regularizers or image priors are key techniques to boost reconstruction precision. The optimal prior generally depends on the subject and the hand-building of priors is hard. A methodology of combining priors to create a better one would be useful for various forms of image processing that use image priors. We propose a theory, called prior ensemble learning (PEL), which combines many weak priors (not limited to images) efficiently and approximates the posterior mean (PM) estimate, which is Bayes optimal for minimizing the mean squared error (MSE). The way of combining priors is changed from that of an exponential family to a mixture family. We applied PEL to an undersampled (10%) multicoil MR image reconstruction task. We demonstrated that PEL could combine 136 image priors (norm-based priors such as total variation (TV) and wavelets with various regularization coefficient (RC) values) from only two training samples and that it was superior to the CS-SENSE-based method in terms of the MSE of the reconstructed image. The resulting combining weights were sparse (18% of the weak priors remained), as expected. By the theory, the PM estimator was decomposed into the sparse weighted sum of each weak prior's PM estimator, and the exponential computational complexity for RCs was reduced to polynomial order w.r.t. the number of weak priors. PEL is feasible and effective for a practical MR image reconstruction task.

Tile-net for undersampled cardiovascular CINE magnetic resonance imaging

We propose the “Tile-net” method based on dividing an image into smaller tiles. Using the tile as the input to the neural network, the network is simplified substantially. The Tile-net learns at a much faster rate than the networks without tiling. The training and reconstruction times for the Tile-net are reduced by 40% and 33%, respectively compared to the networks without tiling. The Tile-net performance is evaluated through the normalized mean square error (NMSE), peak signal to noise ratio (PSNR), structure similarity index measure (SSIM) and the quality of the reconstructed image for test datasets. The Tile-net does not degrade performance; however, it reduces the NMSE by 0.3% compared to the networks without tiling.

Deep frequency-recurrent priors for inverse imaging reconstruction

Ill-posed inverse problems in imaging remain an active research topic in several decades, with new approaches constantly emerging. Recognizing that the popular dictionary learning and convolutional sparse coding are both essentially modeling the high-frequency component of an image, which convey most of the semantic information such as texture details, in this work we propose a novel multi-profile high-frequency transform-guided denoising autoencoder for attaining deep frequency-recurrent prior (DFRP). To achieve this goal, we first extract a set of multi-profile high-frequency components via a specific transformation and add artificial Gaussian noise to these high-frequency components as training samples. Then, as the high-frequency prior information is learned, we incorporate it into classical iterative reconstruction by proximal gradient descent. Preliminary results on highly under-sampled magnetic resonance imaging and sparse-view computed tomography reconstruction demonstrated that the proposed method can efficiently reconstruct feature details and presented advantages over state-of-the-arts.

Comparison of Complex k-Space Data and Magnitude-Only for Training of Deep Learning–Based Artifact Suppression for Real-Time Cine MRI

Propose: The purpose of this study was to compare the performance of deep learning networks trained with complex-valued and magnitude images in suppressing the aliasing artifact for highly accelerated real-time cine MRI.Methods: Two 3D U-net models (Complex-Valued-Net and Magnitude-Net) were implemented to suppress aliasing artifacts in real-time cine images. ECG-segmented cine images (n = 503) generated from both complex k-space data and magnitude-only DICOM were used to synthetize radial real-time cine MRI. Complex-Valued-Net and Magnitude-Net were trained with fully sampled and synthetized radial real-time cine pairs generated from highly undersampled (12-fold) complex k-space and DICOM images, respectively. Real-time cine was prospectively acquired in 29 patients with 12-fold accelerated free-breathing tiny golden-angle radial sequence and reconstructed with both Complex-Valued-Net and Magnitude-Net. Cardiac function, left-ventricular (LV) structure, and subjective image quality [1(non-diagnostic)-5(excellent)] were calculated from Complex-Valued-Net– and Magnitude-Net–reconstructed real-time cine datasets and compared to those of ECG-segmented cine (reference).Results: Free-breathing real-time cine reconstructed by both networks had high correlation (all R2 &amp;gt; 0.7) and good agreement (all p &amp;gt; 0.05) with standard clinical ECG-segmented cine with respect to LV function and structural parameters. Real-time cine reconstructed by Complex-Valued-Net had superior image quality compared to images from Magnitude-Net in terms of myocardial edge sharpness (Complex-Valued-Net = 3.5 ± 0.5; Magnitude-Net = 2.6 ± 0.5), temporal fidelity (Complex-Valued-Net = 3.1 ± 0.4; Magnitude-Net = 2.1 ± 0.4), and artifact suppression (Complex-Valued-Net = 3.1 ± 0.5; Magnitude-Net = 2.0 ± 0.0), which were all inferior to those of ECG-segmented cine (4.1 ± 1.4, 3.9 ± 1.0, and 4.0 ± 1.1).Conclusion: Compared to Magnitude-Net, Complex-Valued-Net produced improved subjective image quality for reconstructed real-time cine images and did not show any difference in quantitative measures of LV function and structure.

Rapid simultaneous acquisition of macromolecular tissue volume, susceptibility, and relaxometry maps.

A major obstacle to the clinical implementation of quantitative MR is the lengthy acquisition time required to derive multi-contrast parametric maps. We sought to reduce the acquisition time for QSM and macromolecular tissue volume by acquiring both contrasts simultaneously by leveraging their redundancies. The joint virtual coil concept with GRAPPA (JVC-GRAPPA) was applied to reduce acquisition time further. Three adult volunteers were imaged on a 3 Tesla scanner using a multi-echo 3D GRE sequence acquired at 3 head orientations. Macromolecular tissue volume, QSM, , T1 , and proton density maps were reconstructed. The same sequence (GRAPPA R = 4) was performed in subject 1 with a single head orientation for comparison. Fully sampled data was acquired in subject 2, from which retrospective undersampling was performed (R = 6 GRAPPA and R = 9 JVC-GRAPPA). Prospective undersampling was performed in subject 3 (R = 6 GRAPPA and R = 9 JVC-GRAPPA) using gradient blips to shift k-space sampling in later echoes. Subject 1's multi-orientation and single-orientation macromolecular tissue volume maps were not significantly different based on RMSE. For subject 2, the retrospectively undersampled JVC-GRAPPA and GRAPPA generated similar results as fully sampled data. This approach was validated with the prospectively undersampled images in subject 3. Using QSM, , and macromolecular tissue volume, the contributions of myelin and iron content to susceptibility were estimated. We have developed a novel strategy to simultaneously acquire data for the reconstruction of 5 intrinsically coregistered 1-mm isotropic resolution multi-parametric maps, with a scan time of 6 min using JVC-GRAPPA.

Fasu-Net: Fast Alzheimer’s Disease Screening with Undersampled MRI Using Convolutional Neural Networks

Alzheimer’s Disease (AD) is a progressive and irreversible neurodegenerative condition, which results in dementia. Mild Cognitive Impairment (MCI) is an intermediate state between normal aging and AD. Instead of traditional questionnaire method, magnetic resonance imaging (MRI) can be used by radiologists to diagnose and screening AD recently, but long acquisition time is not conducive to screening AD and MCI. To solve this problem, we develop a Fasu-Net (Fast Alzheimer’s disease Screening neural network with Undersampled MRI) for AD and MCI clinical classification. The network uses undersampled structural MRI with a shorter acquisition time to improve the screening and diagnosis efficiency of AD. For achieving the best classification result, three axial planes of brain MR images were feed into the Fasu-Net with transfer learning method. The experiment results on undersampled 3D T1-weighted images database (ADNI) show that in the AD versus MCI versus HC (Healthy Controls) classification, the Fasu-Net achieved the accuracy of 91.41%, thus can be a potential method for fast clinical screening of AD.

Global and local constrained parallel MRI reconstruction by exploiting dual sparsity and self-consistency

In this study, we introduce global and local constrained reconstruction for highly undersampled magnetic resonance imaging (MRI). This reconstruction not only exploits dual sparsity and self-consistency constraints, but also effectively decouples them regionally and stepwise. Unlike conventional parallel MRI or compressed sensing (CS), we employed multi-level variable-density k-space sampling, wherein the sampling density becomes sparser from the central to the peripheral region (full-shifted lattice R2-M2 undersampling-incoherent pseudo-random undersampling). Furthermore, complementary local k-space model was introduced as a union of wavelet directional filtered signals and its residual for regionally independent reconstruction, in which wavelet subbands are represented in compact frequency partitions. The subbands were partially leaked over neighboring partitions. To further enhance the accuracy of image details and eliminate potential discrepancies resulting from separate regional reconstructions, selfconsistency constrained reconstruction was performed globally over the entire k-space. Simulations and experimental studies demonstrated that the proposed technique substantially outperforms conventional methods in suppressing artifacts and noise with increasing acceleration factors.

A parallel spatial and Bloch manifold regularized iterative reconstruction method for MR Fingerprinting

Magnetic Resonance Fingerprinting (MRF) reconstructs tissue maps based on a sequence of very highly undersampled images. In order to be able to perform MRF reconstruction, state-of-the-art MRF methods rely on priors such as the MR physics (Bloch equations) and might also use some additional low-rank or spatial regularization. However to our knowledge these three regularizations are not applied together in a joint reconstruction. The reason is that it is indeed challenging to incorporate effectively multiple regularizations in a single MRF optimization algorithm. As a result most of these methods are not robust to noise especially when the sequence length is short. In this paper, we propose a family of new methods where spatial and low-rank regularizations, in addition to the Bloch manifold regularization, are applied on the images. We show on digital phantom and NIST phantom scans, as well as volunteer scans that the proposed methods bring significant improvement in the quality of the estimated tissue maps.

Micrometre-scale strain mapping of transistor arrays extracted from undersampled atomic-resolution images

Strain maps extracted from atomic resolution images have the ultimate spatial resolution, but have a field of view limited by the sampling necessary to resolve atomic lattices. This has typically confined strain maps to dimensions less than ∼100 nanometers. To extend the field of view beyond this limit, we apply a modified geometric phase analysis to undersampled images of atomic lattices (i.e. with a pixel size too large to resolve atomic lattices). To reduce the effects of environmental and instrumental instabilities, the images were obtained by aligning series of rapid annular dark field scanning transmission electron microscopy acquisitions. We demonstrate that for undersampled images, a geometric phase analysis can still be performed on aliased frequencies and, as long as the appropriate scaling matrix is applied, provide accurate atomic displacement measurements at large scale. Experimental challenges related to the increased effects of scanning errors as the magnification is lowered are examined. Although such errors are found to significantly reduce geometric phase signals, it was still possible to produce strain maps for arrays of up to sixteen 20nm-technology transistors, corresponding to a field of view exceeding one micrometer.

End-to-end deep learning nonrigid motion-corrected reconstruction for highly accelerated free-breathing coronary MRA.

To develop an end-to-end deep learning technique for nonrigid motion-corrected (MoCo) reconstruction of ninefold undersampled free-breathing whole-heart coronary MRA (CMRA). A novel deep learning framework was developed consisting of a diffeomorphic registration network and a motion-informed model-based deep learning (MoDL) reconstruction network. The registration network receives as input highly undersampled (~22×) respiratory-resolved images and outputs 3D nonrigid respiratory motion fields between the images. The motion-informed MoDL performs MoCo reconstruction from undersampled data using the predicted motion fields. The whole deep learning framework, termed as MoCo-MoDL, was trained end-to-end in a supervised manner for simultaneous 3D nonrigid motion estimation and MoCo reconstruction. MoCo-MoDL was compared with a state-of-the-art nonrigid MoCo CMRA reconstruction technique in 15 retrospectively undersampled datasets and 9 prospectively undersampled acquisitions. The acquisition time for ninefold accelerated CMRA was ~2.5 min. The reconstruction time was ~22 s for the proposed MoCo-MoDL and ~35 min for the conventional approach. MoCo-MoDL achieved higher peak SNR (27.86 ± 3.00 vs. 26.71 ± 2.79; P < .05) and structural similarity (0.78 ± 0.06 vs. 0.75 ± 0.06; P < .05) than the conventional approach. Similar vessel length and visual image quality score were obtained with the 2 methods, whereas improved vessel sharpness was observed with MoCo-MoDL. An end-to-end deep learning approach was introduced for simultaneous nonrigid motion estimation and MoCo reconstruction of highly undersampled free-breathing whole-heart CMRA. The rapid free-breathing CMRA acquisition together with the fast reconstruction of the proposed approach promises easy integration into clinical workflow.

Dual-Octave Convolution for Accelerated Parallel MR Image Reconstruction

Magnetic resonance (MR) image acquisition is an inherently prolonged process, whose acceleration by obtaining multiple undersampled images simultaneously through parallel imaging has always been the subject of research. In this paper, we propose the Dual-Octave Convolution (Dual-OctConv), which is capable of learning multi-scale spatial-frequency features from both real and imaginary components, for fast parallel MR image reconstruction. By reformulating the complex operations using octave convolutions, our model shows a strong ability to capture richer representations of MR images, while at the same time greatly reducing the spatial redundancy. More specifically, the input feature maps and convolutional kernels are first split into two components (i.e., real and imaginary), which are then divided into four groups according to their spatial frequencies. Then, our Dual-OctConv conducts intra-group information updating and inter-group information exchange to aggregate the contextual information across different groups. Our framework provides two appealing benefits: (i) it encourages interactions between real and imaginary components at various spatial frequencies to achieve richer representational capacity, and (ii) it enlarges the receptive field by learning multiple spatial-frequency features of both the real and imaginary components. We evaluate the performance of the proposed model on the acceleration of multi-coil MR image reconstruction. Extensive experiments are conducted on an {in vivo} knee dataset under different undersampling patterns and acceleration factors. The experimental results demonstrate the superiority of our model in accelerated parallel MR image reconstruction. Our code is available at: github.com/chunmeifeng/Dual-OctConv.

Multiscale Cloud Detection in Remote Sensing Images Using a Dual Convolutional Neural Network

Semantic segmentation by convolutional neural networks (CNN) has advanced the state of the art in pixel-level classification of remote sensing images. However, processing large images typically requires analyzing the image in small patches, and hence features that have large spatial extent still cause challenges in tasks such as cloud masking. To support a wider scale of spatial features while simultaneously reducing computational requirements for large satellite images, we propose an architecture of two cascaded CNN model components successively processing undersampled and full resolution images. The first component distinguishes between patches in the inner cloud area from patches at the cloud's boundary region. For the cloud-ambiguous edge patches requiring further segmentation, the framework then delegates computation to a fine-grained model component. We apply the architecture to a cloud detection dataset of complete Sentinel-2 multispectral images, approximately annotated for minimal false negatives in a land use application. On this specific task and data, we achieve a 16\% relative improvement in pixel accuracy over a CNN baseline based on patching.

Deep image prior for undersampling high-speed photoacoustic microscopy

Photoacoustic microscopy (PAM) is an emerging imaging method combining light and sound. However, limited by the laser’s repetition rate, state-of-the-art high-speed PAM technology often sacrifices spatial sampling density (i.e., undersampling) for increased imaging speed over a large field-of-view. Deep learning (DL) methods have recently been used to improve sparsely sampled PAM images; however, these methods often require time-consuming pre-training and large training dataset with ground truth. Here, we propose the use of deep image prior (DIP) to improve the image quality of undersampled PAM images. Unlike other DL approaches, DIP requires neither pre-training nor fully-sampled ground truth, enabling its flexible and fast implementation on various imaging targets. Our results have demonstrated substantial improvement in PAM images with as few as 1.4 % of the fully sampled pixels on high-speed PAM. Our approach outperforms interpolation, is competitive with pre-trained supervised DL method, and is readily translated to other high-speed, undersampling imaging modalities.

Bayesian uncertainty quantification for magnetic resonance fingerprinting

Magnetic Resonance Fingerprinting (MRF) is a promising technique for fast quantitative imaging of human tissue. In general, MRF is based on a sequence of highly undersampled MR images which are analyzed with a pre-computed dictionary. MRF provides valuable diagnostic parameters such as the T 1 and T 2 MR relaxation times. However, uncertainty characterization of dictionary-based MRF estimates for T 1 and T 2 has not been achieved so far, which makes it challenging to assess if observed differences in these estimates are significant and may indicate pathological changes of the underlying tissue. We propose a Bayesian approach for the uncertainty quantification of dictionary-based MRF which leads to probability distributions for T 1 and T 2 in every voxel. The distributions can be used to make probability statements about the relaxation times, and to assign uncertainties to their dictionary-based MRF estimates. All uncertainty calculations are based on the pre-computed dictionary and the observed sequence of undersampled MR images, and they can be calculated in short time. The approach is explored by analyzing MRF measurements of a phantom consisting of several tubes across which MR relaxation times are constant. The proposed uncertainty quantification is quantitatively consistent with the observed within-tube variability of estimated relaxation times. Furthermore, calculated uncertainties are shown to characterize well observed differences between the MRF estimates and the results obtained from high-accurate reference measurements. These findings indicate that a reliable uncertainty quantification is achieved. We also present results for simulated MRF data and an uncertainty quantification for an in vivo MRF measurement. MATLAB® source code implementing the proposed approach is made available.

Single laser-shot super-resolution photoacoustic tomography with fast sparsity-based reconstruction

Recently, ℓ1-norm based reconstruction approaches have been used with linear array systems to improve photoacoustic resolution and demonstrate undersampled imaging when there is sufficient sparsity in some domain. However, such approaches have yet to beat the half-wavelength resolution limit. In this paper, the ability to beat the half-wavelength diffraction limit is demonstrated using a 5 MHz ring array photoacoustic tomography system and ℓ1-norm based reconstruction approaches. We used the array system to image wire targets at ≈2−3cm depth in both intralipid scattering solution and water. The minimum observable separation was estimated as 70±10μm, improving on the half-wavelength resolution limit of 145μm. This improvement was demonstrated even when using a random projection transform to reduce data by 99%, enabling substantially faster reconstruction times. This is the first photoacoustic tomography approach capable of beating the half-wavelength resolution limit with a single laser shot.

Deep learning-based point-scanning super-resolution imaging.

Point-scanning imaging systems are among the most widely used tools for high-resolution cellular and tissue imaging, benefitting from arbitrarily defined pixel sizes. The resolution, speed, sample preservation, and signal-to-noise ratio (SNR) of point-scanning systems are difficult to optimize simultaneously. We show these limitations can be mitigated via the use of Deep Learning-based supersampling of undersampled images acquired on a point-scanning system, which we term point-scanning super-resolution (PSSR) imaging. We designed a “crappifier” that computationally degrades high SNR, high pixel resolution ground truth images to simulate low SNR, low-resolution counterparts for training PSSR models that can restore real-world undersampled images. For high spatiotemporal resolution fluorescence timelapse data, we developed a “multi-frame” PSSR approach that utilizes information in adjacent frames to improve model predictions. In conclusion, PSSR facilitates point-scanning image acquisition with otherwise unattainable resolution, speed, and sensitivity. All the training data, models, and code for PSSR are publicly available at 3DEM.org.Editor’s summaryPoint-scanning super-resolution imaging uses deep learning to supersample undersampled images and enable time-lapse imaging of subcellular events. An accompanying “crappifier” rapidly generates quality training data for robust performance.

Modeling human observer detection in undersampled magnetic resonance imaging (MRI).

Task-based assessment of image quality in undersampled magnetic resonance imaging (MRI) using constraints is important because of the need to quantify the effect of the artifacts on task performance. Fluid-attenuated inversion recovery (FLAIR) images are used in detection of small metastases in the brain. In this work we carry out two-alternative forced choice (2-AFC) studies with a small signal known exactly (SKE) but with varying background for reconstructed FLAIR images from undersampled multi-coil data. Using a 4x undersampling and a total variation (TV) constraint we found that the human observer detection performance remained fairly constant for a broad range of values in the regularization parameter before decreasing at large values. Using the TV constraint did not improve task performance. The non- prewhitening eye (NPWE) observer and sparse difference-of-Gaussians (S-DOG) observer with internal noise were used to model human observer detection. The parameters for the NPWE and the internal noise for the S-DOG were chosen to match the average percent correct (PC) in 2-AFC studies for three observers using no regularization. The NPWE model observer tracked the performance of the human observers as the regularization was increased but slightly over-estimated the PC for large amounts of regularization. The S-DOG model observer with internal noise tracked human performace for all levels of regularization studied. To our knowledge this is the first time that model observers have been used to track human observer detection for undersampled MRI.

SR-Net: A sequence offset fusion net and refine net for undersampled multislice MR image reconstruction

Background and objective: The study of deep learning-based fast magnetic resonance imaging (MRI) reconstruction methods has become popular in recent years. However, there is still a challenge when MRI results undersample large acceleration factors. The objective of this study was to improve the reconstruction quality of undersampled MR images by exploring data redundancy among slices.Methods: There are two aspects of redundancy in multislice MR images including correlations inside a single slice and correlations among slices. Thus, we built two subnets for the two kinds of redundancy. For correlations among slices, we built a bidirectional recurrent convolutional neural network, named Sequence Offset Fusion Net (S-Net). In S-Net, we used a deformable convolution module to construct a neighbor slice feature extractor. For the correlation inside a single slice, we built a Refine Net (R-Net), which has 5 layers of 2D convolutions. In addition, we used a data consistency (DC) operation to maintain data fidelity in k-space. Finally, we treated the reconstruction task as a dealiasing problem in the image domain, and S-Net and R-Net are applied alternately and iteratively to generate the final reconstructions.Results: The proposed algorithm was evaluated using two online public MRI datasets. Compared with several state-of-the-art methods, the proposed method achieved better reconstruction results in terms of dealiasing and restoring tissue structure. Moreover, with over 14 slices per second reconstruction speed on 256x256 pixel images, the proposed method can meet the need for real-time processing.Conclusion: With spatial correlation among slices as additional prior information, the proposed method dramatically improves the reconstruction quality of undersampled MR images.