Magnetic Resonance Imaging Reconstruction Research Articles

A convex optimisation approach to parallel magnetic resonance imaging reconstruction

A convex optimisation approach to parallel magnetic resonance imaging reconstruction

A convex optimisation approach to parallel magnetic resonance imaging reconstruction

In parallel magnetic resonance imaging (pMRI), the image reconstruction with unknown coil sensitivity functions is known as a non-convex problem in the existing literatures. The analysis of this paper shows that there exists a convex solution region in the space of the magnitude image and sensitivity encoded image functions, which contains the true magnitude image solution. The derivation of the convex solution region resolves the non-convex difficulty and leads to a convex optimisation formulation of the pMRI reconstruction problem. The formulated problem consists of two steps. Each of the steps solves a regularised convex optimisation problem and provides a globally optimal solution, in the sense that the solution optimises the performance index and is independent of the initial conditions. The applications of the proposed two-step optimisation to in vivo and phantom data sets result in superior pMRI reconstruction performance compared with state-of-the-art algorithms.

Accelerated SPIRiT Parallel MR Image Reconstruction Based on Joint Sparsity and Sparsifying Transform Learning

Iterative self-consistent parallel imaging reconstruction (SPIRiT) was an autocalibrating model for parallel magnetic resonance imaging reconstruction, which is often formulated as a SPIRiT reconstruction problem with some regularization terms. Some methods based on the operator splitting and alternating direction method of multipliers (ADMM) have been employed to solve the formulated regularized SPIRiT problem. In this paper, we propose to combine the sparsifying transform learning and joint sparsity with Cartesian SPIRiT parallel magnetic resonance imaging, and solve the resulting reconstruction problem by using the variable splitting and ADMM techniques. Simulation experiments on four in vivo data sets demonstrate that the proposed algorithm achieves a better image reconstruction quality than that of other competing methods. In addition, the proposed algorithm is very suitable for graphics processing unit (GPU) parallel computing, and its accelerated version, achieved by using a GPU, is very fast, requiring only 6.7 s to reconstruct a 200×200 pixel image with 8 channels.

An Efficient Lightweight Generative Adversarial Network for Compressed Sensing Magnetic Resonance Imaging Reconstruction

Compressed-sensing-based magnetic resonance imaging (CS-MRI) methods can significantly shorten scanning time while ensuring reconstructed image quality. Recently, deep learning methods, particularly generative adversarial networks (GAN), have been introduced into CS-MRI. However, these GAN-based methods suffer from their heavy learning parameters and ignore long-range dependency, which degrades the reconstructed image quality. Thus, the objective of this study is to design an efficient lightweight GAN to achieve more accurate MRI reconstruction. The proposed framework, named SepGAN, utilises depthwise separable convolution as the basic component to reduce the number of learning parameters. Two modules, the dilated depthwise separable convolution dense block and a squeeze-and-excitation lightweight self-attention module were proposed to extract the long-range dependency and improve the representational ability. The focal frequency loss was also involved in assisting the model to focus on high-frequency information. To evaluate the performance of the three proposed methods and SepGAN, two brain datasets were used in our experiment. From the results of our comparison analysis, SepGAN possesses the minimum number of parameters and multiply–accumulate operations (i.e., 7.32 M and 13.62G) and outperforms other methods in a variety of evaluation metrics, especially in Frechet inception distance, proving that reconstructed images of our method have better visual effects. For unseen pathological data, SepGAN can also perform effective reconstruction with explicit tumour textures and boundaries. The experimental results demonstrate that SepGAN can reconstruct high quality images with fewer parameters and exhibit remarkable generalisation ability.

On Ambiguity in Linear Inverse Problems: Entrywise Bounds on Nearly Data-Consistent Solutions and Entrywise Condition Numbers.

Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree of ambiguity that may exist about its solution. Traditional measures of ill-posedness, such as the condition number of a matrix, provide characterizations that are global in nature. While such characterizations can be powerful, they can also fail to provide full insight into situations where certain entries of the solution vector are more or less ambiguous than others. In this work, we derive novel theoretical lower- and upper-bounds that apply to individual entries of the solution vector, and are valid for all potential solution vectors that are nearly data-consistent. These bounds are agnostic to the noise statistics and the specific method used to solve the inverse problem, and are also shown to be tight. In addition, our results also lead us to introduce an entrywise version of the traditional condition number, which provides a substantially more nuanced characterization of scenarios where certain elements of the solution vector are less sensitive to perturbations than others. Our results are illustrated in an application to magnetic resonance imaging reconstruction, and we include discussions of practical computation methods for large-scale inverse problems, connections between our new theory and the traditional Cramér-Rao bound under statistical modeling assumptions, and potential extensions to cases involving constraints beyond just data-consistency.

SwinGAN: A dual-domain Swin Transformer-based generative adversarial network for MRI reconstruction

Magnetic resonance imaging (MRI) is one of the most important modalities for clinical diagnosis. However, the main disadvantages of MRI are the long scanning time and the moving artifact caused by patient movement during prolonged imaging. It can also lead to patient anxiety and discomfort, so accelerated imaging is indispensable for MRI. Convolutional neural network (CNN) based methods have become the fact standard for medical image reconstruction, and generative adversarial network (GAN) have also been widely used. Nevertheless, due to the limited ability of CNN to capture long-distance information, it may lead to defects in the structure of the reconstructed images such as blurry contour. In this paper, we propose a novel Swin Transformer-based dual-domain generative adversarial network (SwinGAN) for accelerated MRI reconstruction. The SwinGAN consists of two generators: a frequency-domain generator and an image-domain generator. Both the generators utilize Swin Transformer as backbone for effectively capturing the long-distance dependencies. A contextual image relative position encoder (ciRPE) is designed to enhance the ability to capture local information. We extensively evaluate the method on the IXI brain dataset, MICCAI 2013 dataset and MRNet knee dataset. Compared with KIGAN, the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) are improved by 6.1% and 1.49% to 37.64 dB and 0.98 on IXI dataset respectively, which demonstrates that our model can sufficiently utilize the local and global information of image. The model shows promising performance and robustness under different undersampling masks, different acceleration rates and different datasets. But it needs high hardware requirements with the increasing of the network parameters. The code is available at: https://github.com/learnerzx/SwinGAN.

FFVN: An explicit feature fusion-based variational network for accelerated multi-coil MRI reconstruction

Magnetic Resonance Imaging (MRI) is a leading diagnostic imaging modality that supports high contrast of soft tissues with no invasiveness or radiation. Nonetheless, it suffers from long scan time owing to the inherent physics in its data acquisition process, hampering its development and applications. Traditional strategies such as Compressed Sensing (CS) and Parallel Imaging (PI) allow for MRI acceleration via sub-sampling strategy, and multiple coils, respectively. When Deep Learning (DL) joins in, both strategies get re-vitalized to achieve even faster reconstruction in various reconstruction methods, among which the variational network is a previously proposed method that combines the mathematical structure of variational models with DL for fast MRI reconstruction. However, in our study we observe that the information of MR features is either not efficiently or explicitly exploited in former works based on the variational network. Instead, we introduce a variational network with explicit feature fusion that combines the CS, PI, with DL for accelerated multi-coil MRI reconstruction. By explicitly leveraging the extra information via feature fusion following feature extraction, our proposed method achieves comparably satisfying performance to the state-of-the-art methods without too much computation overhead on a public multi-coil brain dataset under 5-fold and 10-fold acceleration.

De-Aliasing and Accelerated Sparse Magnetic Resonance Image Reconstruction Using Fully Dense CNN with Attention Gates.

When sparsely sampled data are used to accelerate magnetic resonance imaging (MRI), conventional reconstruction approaches produce significant artifacts that obscure the content of the image. To remove aliasing artifacts, we propose an advanced convolutional neural network (CNN) called fully dense attention CNN (FDA-CNN). We updated the Unet model with the fully dense connectivity and attention mechanism for MRI reconstruction. The main benefit of FDA-CNN is that an attention gate in each decoder layer increases the learning process by focusing on the relevant image features and provides a better generalization of the network by reducing irrelevant activations. Moreover, densely interconnected convolutional layers reuse the feature maps and prevent the vanishing gradient problem. Additionally, we also implement a new, proficient under-sampling pattern in the phase direction that takes low and high frequencies from the k-space both randomly and non-randomly. The performance of FDA-CNN was evaluated quantitatively and qualitatively with three different sub-sampling masks and datasets. Compared with five current deep learning-based and two compressed sensing MRI reconstruction techniques, the proposed method performed better as it reconstructed smoother and brighter images. Furthermore, FDA-CNN improved the mean PSNR by 2 dB, SSIM by 0.35, and VIFP by 0.37 compared with Unet for the acceleration factor of 5.

Deep parallel MRI reconstruction based on a complex-valued loss function

To propose a new method for fast MRI reconstruction based on deep learning in parallel MRI data using a new loss function defined as the summation of the mean squared errors of the magnitude and phase. The multicoil image data were combined into single-coil image data to eliminate the correlation between noises and used as a label in the training process. Considering the importance of the phase information in some applications, where the phase information was lost when combining multicoil data using sum of square method, a new loss function was introduced, defined as the weighted sum of the mean squared error (MSE) of the magnitude and phase. The single weight in the loss function was used to balance the importance of the magnitude and phase in different applications. To validate the proposed method, real brain and knee data in FastMRI dataset were used for training and testing. We also compared this proposed method with two other methods that used MSE or mean absolute error (MAE) as a loss function. The experimental results showed that the proposed method was capable of accurate reconstruction of multicoil MR images with significantly reduced artifacts compared with the other two methods. Quantitative analysis showed that the propose method increased the peak signal-to-noise ratio (PSNR) of the reconstructed images by about 1 dB. The proposed deep MRI reconstruction method using a new loss function to fit the noise in parallel MRI data can accelerate MRI reconstruction and significantly improve the quality of the reconstructed images.

An untrained deep learning method for reconstructing dynamic MR images from accelerated model-based data.

To implement physics-based regularization as a stopping condition in tuning an untrained deep neural network for reconstructing MR images from accelerated data. The ConvDecoder (CD) neural network was trained with a physics-based regularization term incorporating the spoiled gradient echo equation that describes variable-flip angle data. Fully-sampled variable-flip angle k-space data were retrospectively accelerated by factors of R={8, 12, 18, 36} and reconstructed with CD, CD with the proposed regularization (CD + r), locally low-rank (LR) reconstruction, and compressed sensing with L1-wavelet regularization (L1). Final images from CD + r training were evaluated at the "argmin" of the regularization loss; whereas the CD, LR, and L1 reconstructions were chosen optimally based on ground truth data. The performance measures used were the normalized RMS error, the concordance correlation coefficient, and the structural similarity index. The CD + r reconstructions, chosen using the stopping condition, yielded structural similarity indexs that were similar to the CD (p=0.47) and LR structural similarity indexs (p=0.95) across R and that were significantly higher than the L1 structural similarity indexs (p=0.04). The concordance correlation coefficient values for the CD + r T1 maps across all R and subjects were greater than those corresponding to the L1 (p=0.15) and LR (p=0.13) T1 maps, respectively. For R ≥ 12 (≤4.2min scan time), L1 and LR T1 maps exhibit a loss of spatially refined details compared to CD + r. The use of an untrained neural network together with a physics-based regularization loss shows promise as a measure for determining the optimal stopping point in training without relying on fully-sampled ground truth data.

Analysis of general weights in weighted ℓ1−2 minimization through applications

The weighted ℓ1−2 minimization has recently attracted some attention due to its capability to deal with highly coherent matrices. Notwithstanding the availability of its stable recovery guarantees, there appear to be some issues not addressed in the literature, which are (i). convergence of the solver for the weighted ℓ1−2 minimization analytically, and (ii). detailed analysis of relevance of general weights to applications. While establishing the convergence of the solver of the weighted ℓ1−2 minimization, we demonstrate the significance of general weights, w∈(0,1), empirically through some applications, including the reconstruction of magnetic resonance images. In particular, we show that the general weights attain significance when we do not have fully accurate or fully corrupt information about the support of the signal to be reconstructed from its linear measurements. We conclude the work by discussing a numerical scheme that chooses the partial support and the weights iteratively.

DMFF-Net: Densely Macroscopic Feature Fusion Network for Fast Magnetic Resonance Image Reconstruction

The task of fast magnetic resonance (MR) image reconstruction is to reconstruct high-quality MR images from undersampled images. Most of the existing methods are based on U-Net, and these methods mainly adopt several simple connections within the network, which we call microscopic design ideas. However, these considerations cannot make full use of the feature information inside the network, which leads to low reconstruction quality. To solve this problem, we rethought the feature utilization method of the encoder and decoder network from a macroscopic point of view and propose a densely macroscopic feature fusion network for fast magnetic resonance image reconstruction. Our network uses three stages to reconstruct high-quality MR images from undersampled images from coarse to fine. We propose an inter-stage feature compensation structure (IFCS) which makes full use of the feature information of different stages and fuses the features of different encoders and decoders. This structure uses a connection method between sub-networks similar to dense form to fuse encoding and decoding features, which is called densely macroscopic feature fusion. A cross network attention block (CNAB) is also proposed to further improve the reconstruction performance. Experiments show that the quality of undersampled MR images is greatly improved, and the detailed information of MR images is enriched to a large extent. Our reconstruction network is lighter than many previous methods, but it achieves better performance. The performance of our method is about 10% higher than that of the original method, and about 3% higher than that of most existing methods. Compared with the nearest optimal algorithms, the performance of our method is improved by about 0.01–0.45%, and our computational complexity is only 1/14 of these algorithms.

MR image reconstruction from undersampled data for image-guided radiation therapy using a patient-specific deep manifold image prior.

Recent advancements in radiotherapy (RT) have allowed for the integration of a Magnetic Resonance (MR) imaging scanner with a medical linear accelerator to use MR images for image guidance to position tumors against the treatment beam. Undersampling in MR acquisition is desired to accelerate the imaging process, but unavoidably deteriorates the reconstructed image quality. In RT, a high-quality MR image of a patient is available for treatment planning. In light of this unique clinical scenario, we proposed to exploit the patient-specific image prior to facilitate high-quality MR image reconstruction. Utilizing the planning MR image, we established a deep auto-encoder to form a manifold of image patches of the patient. The trained manifold was then incorporated as a regularization to restore MR images of the same patient from undersampled data. We performed a simulation study using a patient case, a real patient study with three liver cancer patient cases, and a phantom experimental study using data acquired on an in-house small animal MR scanner. We compared the performance of the proposed method with those of the Fourier transform method, a tight-frame based Compressive Sensing method, and a deep learning method with a patient-generic manifold as the image prior. In the simulation study with 12.5% radial undersampling and 15% increase in noise, our method improved peak-signal-to-noise ratio by 4.46dB and structural similarity index measure by 28% compared to the patient-generic manifold method. In the experimental study, our method outperformed others by producing reconstructions of visually improved image quality.

Magnetic resonance imaging reconstruction using a deep energy-based model.

Although recent deep energy-based generative models (EBMs) have shown encouraging results in many image-generation tasks, how to take advantage of self-adversarial cogitation in deep EBMs to boost the performance of magnetic resonance imaging (MRI) reconstruction is still desired. With the successful application of deep learning in a wide range of MRI reconstructions, a line of emerging research involves formulating an optimization-based reconstruction method in the space of a generative model. Leveraging this, a novel regularization strategy is introduced in this article that takes advantage of self-adversarial cogitation of the deep energy-based model. More precisely, we advocate alternating learning by a more powerful energy-based model with maximum likelihood estimation to obtain the deep energy-based information, represented as a prior image. Simultaneously, implicit inference with Langevin dynamics is a unique property of reconstruction. In contrast to other generative models for reconstruction, the proposed method utilizes deep energy-based information as the image prior in reconstruction to improve the quality of image. Experimental results imply the proposed technique can obtain remarkable performance in terms of high reconstruction accuracy that is competitive with state-of-the-art methods, and which does not suffer from mode collapse. Algorithmically, an iterative approach is presented to strengthen EBM training with the gradient of energy network. The robustness and reproducibility of the algorithm were also experimentally validated. More importantly, the proposed reconstruction framework can be generalized for most MRI reconstruction scenarios.

A novel data-driven method for the analysis and reconstruction of cardiac cine MRI

Cardiac cine magnetic resonance imaging (MRI) can be considered the optimal criterion for measuring cardiac function. This imaging technique can provide us with detailed information about cardiac structure, tissue composition and even blood flow, which makes it highly used in medical science. But due to the image time acquisition and several other factors the MRI sequences can easily get corrupted, causing radiologists to misdiagnose 40 million people worldwide each and every single year. Hence, the urge to decrease these numbers, researchers from different fields have been introducing novel tools and methods in the medical field. Aiming to the same target, we consider in this work the application of the higher order dynamic mode decomposition (HODMD) technique. The HODMD algorithm is a linear method, which was originally introduced in the fluid dynamics domain, for the analysis of complex systems. Nevertheless, the proposed method has extended its applicability to numerous domains, including medicine. In this work, HODMD in used to analyze sets of MR images of a heart, with the ultimate goal of identifying the main patterns and frequencies driving the heart dynamics. Furthermore, a novel interpolation algorithm based on singular value decomposition combined with HODMD is introduced, providing a three-dimensional reconstruction of the heart. This algorithm is applied (i) to reconstruct corrupted or missing images, and (ii) to build a reduced order model of the heart dynamics.

Accelerated Diffusion-Weighted MR Image Reconstruction Using Deep Neural Networks

Under-sampling in diffusion-weighted imaging (DWI) decreases the scan time that helps to reduce off-resonance effects, geometric distortions, and susceptibility artifacts; however, it leads to under-sampling artifacts. In this paper, diffusion-weighted MR image (DWI-MR) reconstruction using deep learning (DWI U-Net) is proposed to recover artifact-free DW images from variable density highly under-sampled k-space data. Additionally, different optimizers, i.e., RMSProp, Adam, Adagrad, and Adadelta, have been investigated to choose the best optimizers for DWI U-Net. The reconstruction results are compared with the conventional Compressed Sensing (CS) reconstruction. The quality of the recovered images is assessed using mean artifact power (AP), mean root mean square error (RMSE), mean structural similarity index measure (SSIM), and mean apparent diffusion coefficient (ADC). The proposed method provides up to 61.1%, 60.0%, 30.4%, and 28.7% improvements in the mean AP value of the reconstructed images in our experiments with different optimizers, i.e., RMSProp, Adam, Adagrad, and Adadelta, respectively, as compared to the conventional CS at an acceleration factor of 6 (i.e., AF = 6). The results of DWI U-Net with the RMSProp, Adam, Adagrad, and Adadelta optimizers show 13.6%, 10.0%, 8.7%, and 8.74% improvements, respectively, in terms of mean SSIM with respect to the conventional CS at AF = 6. Also, the proposed technique shows 51.4%, 29.5%, 24.04%, and 18.0% improvements in terms of mean RMSE using the RMSProp, Adam, Adagrad, and Adadelta optimizers, respectively, with reference to the conventional CS at AF = 6. The results confirm that DWI U-Net performs better than the conventional CS reconstruction. Also, when comparing the different optimizers in DWI U-Net, RMSProp provides better results than the other optimizers.

SelfCoLearn: Self-Supervised Collaborative Learning for Accelerating Dynamic MR Imaging.

Lately, deep learning technology has been extensively investigated for accelerating dynamic magnetic resonance (MR) imaging, with encouraging progresses achieved. However, without fully sampled reference data for training, the current approaches may have limited abilities in recovering fine details or structures. To address this challenge, this paper proposes a self-supervised collaborative learning framework (SelfCoLearn) for accurate dynamic MR image reconstruction from undersampled k-space data directly. The proposed SelfCoLearn is equipped with three important components, namely, dual-network collaborative learning, reunderampling data augmentation and a special-designed co-training loss. The framework is flexible and can be integrated into various model-based iterative un-rolled networks. The proposed method has been evaluated on an in vivo dataset and was compared to four state-of-the-art methods. The results show that the proposed method possesses strong capabilities in capturing essential and inherent representations for direct reconstructions from the undersampled k-space data and thus enables high-quality and fast dynamic MR imaging.

Generalized self-calibrating simultaneous multi-slice MR image reconstruction from 3D Fourier encoding perspective.

This work introduces a novel, k-space based one-step solution for simultaneous multi-slice MR image reconstruction from 3D Fourier encoding perspective. With undersampled SMS imaging, image reconstruction suffers from both inter-slice leakages and in-plane aliasing artifacts. Aliasing separation becomes further challenging in the presence of discrepancies between calibration and imaging. To address them, in this work a measured SMS 3D k-space with additional calibrating signals is decomposed into SMS imaging and self-calibrating data sets. Extended controlled aliasing is performed by upsampling the measured data in the kz-direction. A slice-specific null space operator is then learned using extended self-calibration exploiting target slices and additional in-plane-shifted images. Inter-slice leakages and in-plane aliasing artifacts are jointly resolved in a single step by solving a constrained optimization problem in which null space reconstruction consistency is balanced with a Hankel-structured low rank prior while data fidelity in 3D Fourier space is enforced. Retrospective and prospective studies are performed to validate the effectiveness of the proposed method in various regions including knee and L-spine.

Transferring Deep Gaussian Denoiser for Compressed Sensing MRI Reconstruction

Deep neural networks have achieved the most outstanding performance in compressed sensing magnetic resonance imaging (CS-MRI) reconstruction by learning the potential structures of images from a large number of training samples. However, the required data comprising hundreds of subjects are usually rare. In this article, we remedy this problem by transferring the easy-to-get deep Gaussian denoisers trained with natural images for artifact reduction in the iterative recovery process without the use of full-sampled MRI data. To this end, we first train a set of deep Gaussian networks with natural images and then incorporate them into a play-and-plug framework that is built by modifying the proximal gradient algorithm with the classical momentum strategy. Furthermore, a nonlocal denoiser is employed for efficiently removing the artifacts. It is found that the momentum strategy can make the statistical distribution of artifacts approximately be Gaussian, making the Gaussian denoisers available for CS-MRI. In the experiments, we verify the rationality of the established framework and show that our method consistently outperforms state-of-the-art methods.

An End-to-End Recurrent Neural Network for Radial MR Image Reconstruction.

Recent advances in deep learning have contributed greatly to the field of parallel MR imaging, where a reduced amount of k-space data are acquired to accelerate imaging time. In our previous work, we have proposed a deep learning method to reconstruct MR images directly from k-space data acquired with Cartesian trajectories. However, MRI utilizes various non-Cartesian trajectories, such as radial trajectories, with various numbers of multi-channel RF coils according to the purpose of an MRI scan. Thus, it is important for a reconstruction network to efficiently unfold aliasing artifacts due to undersampling and to combine multi-channel k-space data into single-channel data. In this work, a neural network named ‘ETER-net’ is utilized to reconstruct an MR image directly from k-space data acquired with Cartesian and non-Cartesian trajectories and multi-channel RF coils. In the proposed image reconstruction network, the domain transform network converts k-space data into a rough image, which is then refined in the following network to reconstruct a final image. We also analyze loss functions including adversarial and perceptual losses to improve the network performance. For experiments, we acquired k-space data at a 3T MRI scanner with Cartesian and radial trajectories to show the learning mechanism of the direct mapping relationship between the k-space and the corresponding image by the proposed network and to demonstrate the practical applications. According to our experiments, the proposed method showed satisfactory performance in reconstructing images from undersampled single- or multi-channel k-space data with reduced image artifacts. In conclusion, the proposed method is a deep-learning-based MR reconstruction network, which can be used as a unified solution for parallel MRI, where k-space data are acquired with various scanning trajectories.