Parallel Magnetic Resonance Imaging Reconstruction Research Articles

FCSSL: fusion enhanced contrastive self-supervised learning method for parallel MRI reconstruction

Objective. The implementation of deep learning in magnetic resonance imaging (MRI) has significantly advanced the reduction of data acquisition times. However, these techniques face substantial limitations in scenarios where acquiring fully sampled datasets is unfeasible or costly.Approach. To tackle this problem, we propose a fusion enhanced contrastive self-supervised learning (FCSSL) method for parallel MRI reconstruction, eliminating the need for fully sampledk-space training dataset and coil sensitivity maps. First, we introduce a strategy based on two pairs of re-undersampling masks within a contrastive learning framework, aimed at enhancing the representational capacity to achieve higher quality reconstruction. Subsequently, a novel adaptive fusion network, trained in a self-supervised learning manner, is designed to integrate the reconstruction results of the framework.Results. Experimental results on knee datasets under different sampling masks demonstrate that the proposed FCSSL achieves superior reconstruction performance compared to other self-supervised learning methods. Moreover,the performance of FCSSL approaches that of the supervised methods, especially under the 2DRU and RADU masks, but no need for fully sample data. The proposed FCSSL, trained under the 3× 1DRU and 2DRU masks, can effectively generalize to unseen 1D and 2D undersampling masks, respectively. For target domain data that exhibit significant differences from source domain data, the proposed model, fine-tuned with just a few dozen instances of undersampled data in the target domain, achieves reconstruction performance comparable to that achieved by the model trained with the entire set of undersampled data.Significance. The novel FCSSL model offers a viable solution for reconstructing high-quality MR images without needing fully sampled datasets, thereby overcoming a major hurdle in scenarios where acquiring fully sampled MR data is difficult.

VSHARP: Variable Splitting Half-quadratic ADMM algorithm for reconstruction of inverse-problems

Medical Imaging (MI) tasks, such as accelerated parallel Magnetic Resonance Imaging (MRI), often involve reconstructing an image from noisy or incomplete measurements. This amounts to solving ill-posed inverse problems, where a satisfactory closed-form analytical solution is not available. Traditional methods such as Compressed Sensing (CS) in MRI reconstruction can be time-consuming or prone to obtaining low-fidelity images. Recently, a plethora of Deep Learning (DL) approaches have demonstrated superior performance in inverse-problem solving, surpassing conventional methods. In this study, we propose vSHARP (variable Splitting Half-quadratic ADMM algorithm for Reconstruction of inverse Problems), a novel DL-based method for solving ill-posed inverse problems arising in MI. vSHARP utilizes the Half-Quadratic Variable Splitting method and employs the Alternating Direction Method of Multipliers (ADMM) to unroll the optimization process. For data consistency, vSHARP unrolls a differentiable gradient descent process in the image domain, while a DL-based denoiser, such as a U-Net architecture, is applied to enhance image quality. vSHARP also employs a dilated-convolution DL-based model to predict the Lagrange multipliers for the ADMM initialization. We evaluate vSHARP on tasks of accelerated parallel MRI Reconstruction using two distinct datasets and on accelerated parallel dynamic MRI Reconstruction using another dataset. Our comparative analysis with state-of-the-art methods demonstrates the superior performance of vSHARP in these applications.

DFUSNN: zero-shot dual-domain fusion unsupervised neural network for parallel MRI reconstruction

Objective. Recently, deep learning models have been used to reconstruct parallel magnetic resonance (MR) images from undersampled k-space data. However, most existing approaches depend on large databases of fully sampled MR data for training, which can be challenging or sometimes infeasible to acquire in certain scenarios. The goal is to develop an effective alternative for improved reconstruction quality that does not rely on external training datasets. Approach. We introduce a novel zero-shot dual-domain fusion unsupervised neural network (DFUSNN) for parallel MR imaging reconstruction without any external training datasets. We employ the Noise2Noise (N2N) network for the reconstruction in the k-space domain, integrate phase and coil sensitivity smoothness priors into the k-space N2N network, and use an early stopping criterion to prevent overfitting. Additionally, we propose a dual-domain fusion method based on Bayesian optimization to enhance reconstruction quality efficiently. Results. Simulation experiments conducted on three datasets with different undersampling patterns showed that the DFUSNN outperforms all other competing unsupervised methods and the one-shot Hankel-k-space generative model (HKGM). The DFUSNN also achieves comparable results to the supervised Deep-SLR method. Significance. The novel DFUSNN model offers a viable solution for reconstructing high-quality MR images without the need for external training datasets, thereby overcoming a major hurdle in scenarios where acquiring fully sampled MR data is difficult.

IMJENSE: Scan-Specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI.

Parallel imaging is a commonly used technique to accelerate magnetic resonance imaging (MRI) data acquisition. Mathematically, parallel MRI reconstruction can be formulated as an inverse problem relating the sparsely sampled k-space measurements to the desired MRI image. Despite the success of many existing reconstruction algorithms, it remains a challenge to reliably reconstruct a high-quality image from highly reduced k-space measurements. Recently, implicit neural representation has emerged as a powerful paradigm to exploit the internal information and the physics of partially acquired data to generate the desired object. In this study, we introduced IMJENSE, a scan-specific implicit neural representation-based method for improving parallel MRI reconstruction. Specifically, the underlying MRI image and coil sensitivities were modeled as continuous functions of spatial coordinates, parameterized by neural networks and polynomials, respectively. The weights in the networks and coefficients in the polynomials were simultaneously learned directly from sparsely acquired k-space measurements, without fully sampled ground truth data for training. Benefiting from the powerful continuous representation and joint estimation of the MRI image and coil sensitivities, IMJENSE outperforms conventional image or k-space domain reconstruction algorithms. With extremely limited calibration data, IMJENSE is more stable than supervised calibrationless and calibration-based deep-learning methods. Results show that IMJENSE robustly reconstructs the images acquired at 5× and 6× accelerations with only 4 or 8 calibration lines in 2D Cartesian acquisitions, corresponding to 22.0% and 19.5% undersampling rates. The high-quality results and scanning specificity make the proposed method hold the potential for further accelerating the data acquisition of parallel MRI.

Improved Complex Convolutional Neural Network Based on SPIRiT and Dense Connection for Parallel MRI Reconstruction

To accelerate the data acquisition speed of magnetic resonance imaging (MRI) and improve the reconstructed MR images’ quality, we propose a parallel MRI reconstruction model (SPIRiT-Net), which combines the iterative self-consistent parallel imaging reconstruction model (SPIRiT) with the cascaded complex convolutional neural networks (CCNNs). More specifically, this model adopts the SPIRiT model for reconstruction in the k-space domain and the cascaded CCNNs with dense connection for reconstruction in the image domain. Meanwhile, this model introduces the data consistency layers for better reconstruction in both the image domain and the k-space domain. The experimental results on two clinical knee datasets as well as the fastMRI brain dataset under different undersampling patterns show that the SPIRiT-Net model achieves better reconstruction performance in terms of visual effect, peak signal-to-noise ratio, and structural similarity over SPIRiT, Deepcomplex, and DONet. It will be beneficial to the diagnosis of clinical medicine.

DONet: Dual-Octave Network for Fast MR Image Reconstruction.

Magnetic resonance (MR) image acquisition is an inherently prolonged process, whose acceleration has long been the subject of research. This is commonly achieved by obtaining multiple undersampled images, simultaneously, through parallel imaging. In this article, we propose the dual-octave network (DONet), which is capable of learning multiscale spatial-frequency features from both the real and imaginary components of MR data, for parallel fast MR image reconstruction. More specifically, our DONet consists of a series of dual-octave convolutions (Dual-OctConvs), which are connected in a dense manner for better reuse of features. In each Dual-OctConv, the input feature maps and convolutional kernels are first split into two components (i.e., real and imaginary) and then divided into four groups according to their spatial frequencies. Then, our Dual-OctConv conducts intragroup information updating and intergroup information exchange to aggregate the contextual information across different groups. Our framework provides three appealing benefits: 1) it encourages information interaction and fusion between the real and imaginary components at various spatial frequencies to achieve richer representational capacity; 2) the dense connections between the real and imaginary groups in each Dual-OctConv make the propagation of features more efficient by feature reuse; and 3) DONet enlarges the receptive field by learning multiple spatial-frequency features of both the real and imaginary components. Extensive experiments on two popular datasets (i.e., clinical knee and fastMRI), under different undersampling patterns and acceleration factors, demonstrate the superiority of our model in accelerated parallel MR image reconstruction.

Improved Sensitivity Encoding Parallel Magnetic Resonance Imaging Reconstruction Algorithm Based on Efficient Sum of Outer Products Dictionary Learning

Improved Sensitivity Encoding Parallel Magnetic Resonance Imaging Reconstruction Algorithm Based on Efficient Sum of Outer Products Dictionary Learning

Fast Parallel Magnetic Resonance Imaging Reconstruction Based on Sparsifying Transform Learning and Structured Low-Rank Model

Fast Parallel Magnetic Resonance Imaging Reconstruction Based on Sparsifying Transform Learning and Structured Low-Rank Model

Improved Parallel Magnetic Resonance Imaging Reconstruction with Sampling based on Normal Distribution

Generalized autocalibrating partially parallel acquisitions (GRAPPA) is a k-space-based magnetic resonance imaging (MRI) reconstruction algorithm that obtains coefficients by acquiring k-space center data with the Nyquist frequency requirement, fitting these data as auto-calibration signal (ACS). The under-sampled k-space data are then filled using the linear correlation of the neighboring points of the k-space. At high reduction factors, images reconstructed by using GRAPPA have high levels of noise even when the number of ACS lines is significantly increased. NL-GRAPPA (Non-linear GRAPPA) can improve GRAPPA for a comparatively impressive image quality. However, it is extremely difficult to reduce the sampling time significantly because of the high number of ACS lines that must be sampled. In this paper, we proposed an undersampling parallel MRI (pMRI) reconstruction technique based on the ideology of normal distribution to improve the traditional GRAPPA and NL-GRAPPA methods. The proposed method mainly takes advantage of the fact that the data in the center of the k-space had a greater impact on the imaging quality than the data at the edges, and then samples the data based on the ideology of normal distribution, i.e., discarding part of the data at the edges of the k-space. The experimental results show that our proposed method can significantly reduce the number of sampled lines and have higher imaging quality with a lower number of ACS lines.

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.

A miniature U-net for k-space-based parallel magnetic resonance imaging reconstruction with a mixed loss function.

BackgroundDeep learning-based magnetic resonance imaging (MRI) methods require in most cases a separate dataset with thousands of images for each anatomical site to train the network model. This paper proposes a miniature U-net method for k-space-based parallel MRI where the network model is trained individually for each scan using scan-specific autocalibrating signal data.MethodsThe original U-net was tailored with fewer layers and channels, and the network was trained using the autocalibrating signal data with a mixing loss function involving magnitude loss and phase loss. The performance of the proposed method was measured using both phantom and in vivo datasets compared to scan-specific robust artificial-neural-networks for k-space interpolation (RAKI) and generalized autocalibrating partially parallel acquisitions (GRAPPA).ResultsThe proposed method alleviates aliasing artifacts and reduces noise with an acceleration factor of four for phantom and in vivo data. Compared with RAKI and GRAPPA, the proposed method represents an improvement with a structural similarity index measure of between 0.02 and 0.05 and a peak signal-to-noise ratio (PSNR) of between 0.1 and 3.ConclusionsThe proposed method introduces a miniature U-net to reconstruct the missing k-space data, which can provide an optimal trade-off between network performance and requirement of training samples. Experimental results indicate that the proposed method can improve image quality compared with the deep learning-based k-space parallel magnitude resonance imaging method.

A tailor-made 3-dimensional directional Haar semi-tight framelet for pMRI reconstruction

In this paper, we propose a model for parallel magnetic resonance imaging (pMRI) reconstruction, regularized by a carefully designed tight framelet system, that can lead to reconstructed images with much less artifacts in comparison to those from existing models. Our model is motivated from the observations that each receiver coil in a pMRI system is more sensitive to the specific object nearest to the coil, and all coil images are correlated. To exploit these observations, we first stack all coil images together as a 3-dimensional (3D) data matrix, and then design a 3D directional Haar tight framelet (3DHTF) to represent it. After analyzing sparse information of the coil images provided by the high-pass filters of the 3DHTF, we separate the high-pass filters into effective ones and ineffective ones, and we then devise a 3D directional Haar semi-tight framelet (3DHSTF) from the 3DHTF by replacing its ineffective filters with only one filter. This 3DHSTF is tailor-made for coil images, meanwhile, giving a significant saving in computation comparing to the 3DHTF. With the 3DHSTF, we propose an ℓ 1 -3DHSTF model for pMRI reconstruction. Numerical experiments for MRI phantom and in-vivo data sets are provided to demonstrate the superiority of our ℓ 1 -3DHSTF model in terms of the efficiency of reducing aliasing artifacts in the reconstructed images.

Iterative self-consistent parallel magnetic resonance imaging reconstruction based on nonlocal low-rank regularization

Iterative self-consistent parallel imaging reconstruction (SPIRiT) is an effective self-calibrated reconstruction model for parallel magnetic resonance imaging (PMRI). The joint L1 norm of wavelet or tight frame coefficients and joint total variation (TV) regularization terms are incorporated into the SPIRiT model to improve the reconstruction performance. The simultaneous two-directional low-rankness (STDLR) in k-space data is incorporated into SPIRiT to realize improved reconstruction. Recent methods have exploited the nonlocal self-similarity (NSS) of images by imposing nonlocal low-rankness of similar patches to achieve a superior performance. To fully utilize both the NSS in Magnetic resonance (MR) images and calibration consistency in the k-space domain, we propose a nonlocal low-rank (NLR)-SPIRiT model by incorporating NLR regularization into the SPIRiT model. We apply the weighted nuclear norm (WNN) as a surrogate of the rank and employ the Nash equilibrium (NE) formulation and alternating direction method of multipliers (ADMM) to efficiently solve the NLR-SPIRiT model. The experimental results demonstrate the superior performance of NLR-SPIRiT over the state-of-the-art methods via three objective metrics and visual comparison.

Parallel MRI Reconstruction Using Broad Learning System.

As an inverse problem, parallel magnetic resonance imaging (pMRI) reconstruction accelerates imaging speed by interpolating missing k-space data from a group of phased-array coils. Deep learning methods have been used for improving pMRI reconstruction quality in recent years. However, deep learning approaches need a large amount of training data that are acquired from different hardware configurations and anatomical areas. Data distributions may be different between training data and testing data, and a long-time training is needed. In this work, we proposed a broad learning system based parallel MRI reconstruction that exploits approximation capability of one-layer neural network through broadening network structure with expanded nodes. Experimental results show that the proposed method is able to suppress noise in compared to the conventional pMRI reconstruction.

Domain knowledge augmentation of parallel MR image reconstruction using deep learning.

A deep learning (DL) method for accelerated magnetic resonance (MR) imaging is presented that incorporates domain knowledge of parallel MR imaging to augment the DL networks for accurate and stable image reconstruction. The proposed DL method employs a novel loss function consisting of a combination of mean absolute error, structural similarity, and sobel edge loss. The DL model takes both original measurements and images reconstructed by the parallel imaging method as inputs to the network. The accuracy of the proposed method was evaluated using two anatomical regions and six MRI contrasts and was compared with state-of-the-art parallel imaging and deep learning methods. The proposed method significantly outperformed the other methods for all the six different contrasts in terms of structural similarity, peak signal to noise ratio, and normalized mean squared error. The out-of-sample performance of the proposed method was assessed for a truly "unseen" case in a volunteer scan. The method produced images without any artificial features, often occurring in the DL image reconstruction methods. A stability analysis was performed by adding perturbations to the input, which demonstrated that the proposed method is robust and stable with respect to small structural changes, and different undersampling ratios. Comprehensive validation on large datasets demonstrated that incorporation of domain knowledge sufficiently regularizes the DL based image reconstruction and produces accurate and stable image enhancement.

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.

Systematic evaluation of iterative deep neural networks for fast parallel MRI reconstruction with sensitivity-weighted coil combination.

To systematically investigate the influence of various data consistency layers and regularization networks with respect to variations in the training and test data domain, for sensitivity-encoded accelerated parallel MR image reconstruction. Magnetic resonance (MR) image reconstruction is formulated as a learned unrolled optimization scheme with a down-up network as regularization and varying data consistency layers. The proposed networks are compared to other state-of-the-art approaches on the publicly available fastMRI knee and neuro dataset and tested for stability across different training configurations regarding anatomy and number of training samples. Data consistency layers and expressive regularization networks, such as the proposed down-up networks, form the cornerstone for robust MR image reconstruction. Physics-based reconstruction networks outperform post-processing methods substantially for R=4 in all cases and for R=8 when the training and test data are aligned. At R=8, aligning training and test data is more important than architectural choices. In this work, we study how dataset sizes affect single-anatomy and cross-anatomy training of neural networks for MRI reconstruction. The study provides insights into the robustness, properties, and acceleration limits of state-of-the-art networks, and our proposed down-up networks. These key insights provide essential aspects to successfully translate learning-based MRI reconstruction to clinical practice, where we are confronted with limited datasets and various imaged anatomies.

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.