Paired Dictionary Learning Based MR Image Reconstruction from Undersampled k-Space Data

Deep model-based magnetic resonance parameter mapping network (DOPAMINE) for fast T1 mapping using variable flip angle method.

Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data. Graphical abstract Two Real Images and their sparsified images by singularizing operator.

Compressed sensing (CS) algorithms exploit sparseness properties to reconstruct high spatial resolution magnetic resonance (MR) images from k-space data acquisitions significantly under sampled to reduce imaging times. CS algorithm effectiveness is frequently shown using under-sampled k-space data from NxN simulated images. These demonstration reconstructions are near perfect with quality higher than reconstructions using under-sampled NxN experimental k-space data sets. These differences are explained in terms of the interaction between the explicit transform domain sparsity requirement employed during iterative CS reconstruction and an inherent frequency domain property of the discrete Fourier transform (DFT). We report on experiments to overcome the limitations imposed by this DFT property by modifying the CS objective function to use a sparseness transform with a resolution higher that the standard transform related to the acquired NxN data matrix size. We demonstrate the relative effectiveness and limitations of standard CS and our proposed highresolution k-space extrapolation enabled (Hi-KEE) CS reconstruction on underand fully-sampled, simulated and experimental MR k-space data. (8 pages)

Using High-Pass Filter to Enhance Scan Specific Learning for MRI Reconstruction without Any Extra Training Data

The deep learning method is an efficient solution for improving the quality of undersampled magnetic resonance (MR) image reconstruction while reducing lengthy data acquisition. Most deep learning methods neglect the mutual constraints between the real and imaginary components of complex-valued k-space data. In this paper, a new complex-valued convolutional neural network, namely, Dense-U-Dense Net (DUD-Net), is proposed to interpolate the undersampled k-space data and reconstruct MR images. The proposed network comprises dense layers, U-Net, and other dense layers in sequence. The dense layers are used to simulate the mutual constraints between real and imaginary components, and U-Net performs feature sparsity and interpolation estimation for k-space data. Two MRI datasets were used to evaluate the proposed method: brain magnitude-only MR images and knee complex-valued k-space data. Several operations were conducted for data preprocessing. First, the complex-valued MR images were synthesized by phase modulation on magnitude-only images. Second, a radial trajectory based on the golden angle was used for k-space undersampling, whereby a reversible normalization method was proposed to balance the distribution of positive and negative values in k-space data. The optimal performance of DUD-Net was demonstrated based on a quantitative evaluation of inter-method and intra-method comparisons. When compared with other methods, significant improvements were achieved, PSNRs were increased by 10.78 and 5.74dB, whereas RMSEs were decreased by 71.53% and 30.31% for magnitude and phase image, respectively. It is concluded that DUD-Net significantly improves the performance of MR image reconstruction.

The extended acquisition times required for MRI limit its availability in resource-constrained settings. Consequently, accelerating MRI by undersampling k-space data, which is necessary to reconstruct an image, has been a long-standing but important challenge. We aimed to develop a deep convolutional neural network (dCNN) optimisation method for MRI reconstruction and to reduce scan times and evaluate its effect on image quality and accuracy of oncological imaging biomarkers. In this multicentre, retrospective, cohort study, MRI data from patients with glioblastoma treated at Heidelberg University Hospital (775 patients and 775 examinations) and from the phase 2 CORE trial (260 patients, 1083 examinations, and 58 institutions) and the phase 3 CENTRIC trial (505 patients, 3147 examinations, and 139 institutions) were used to develop, train, and test dCNN for reconstructing MRI from highly undersampled single-coil k-space data with various acceleration rates (R=2, 4, 6, 8, 10, and 15). Independent testing was performed with MRIs from the phase 2/3 EORTC-26101 trial (528 patients with glioblastoma, 1974 examinations, and 32 institutions). The similarity between undersampled dCNN-reconstructed and original MRIs was quantified with various image quality metrics, including structural similarity index measure (SSIM) and the accuracy of undersampled dCNN-reconstructed MRI on downstream radiological assessment of imaging biomarkers in oncology (automated artificial intelligence-based quantification of tumour burden and treatment response) was performed in the EORTC-26101 test dataset. The public NYU Langone Health fastMRI brain test dataset (558 patients and 558 examinations) was used to validate the generalisability and robustness of the dCNN for reconstructing MRIs from available multi-coil (parallel imaging) k-space data. In the EORTC-26101 test dataset, the median SSIM of undersampled dCNN-reconstructed MRI ranged from 0·88 to 0·99 across different acceleration rates, with 0·92 (95% CI 0·92-0·93) for 10-times acceleration (R=10). The 10-times undersampled dCNN-reconstructed MRI yielded excellent agreement with original MRI when assessing volumes of contrast-enhancing tumour (median DICE for spatial agreement of 0·89 [95% CI 0·88 to 0·89]; median volume difference of 0·01 cm3 [95% CI 0·00 to 0·03] equalling 0·21%; p=0·0036 for equivalence) or non-enhancing tumour or oedema (median DICE of 0·94 [95% CI 0·94 to 0·95]; median volume difference of -0·79 cm3 [95% CI -0·87 to -0·72] equalling -1·77%; p=0·023 for equivalence) in the EORTC-26101 test dataset. Automated volumetric tumour response assessment in the EORTC-26101 test dataset yielded an identical median time to progression of 4·27 months (95% CI 4·14 to 4·57) when using 10-times-undersampled dCNN-reconstructed or original MRI (log-rank p=0·80) and agreement in the time to progression in 374 (95·2%) of 393 patients with data. The dCNN generalised well to the fastMRI brain dataset, with significant improvements in the median SSIM when using multi-coil compared with single-coil k-space data (p<0·0001). Deep-learning-based reconstruction of undersampled MRI allows for a substantial reduction of scan times, with a 10-times acceleration demonstrating excellent image quality while preserving the accuracy of derived imaging biomarkers for the assessment of oncological treatment response. Our developments are available as open source software and hold considerable promise for increasing the accessibility to MRI, pending further prospective validation. Deutsche Forschungsgemeinschaft (German Research Foundation) and an Else Kröner Clinician Scientist Endowed Professorship by the Else Kröner Fresenius Foundation.

To review the latest developments in self-supervised deep learning (DL) techniques for magnetic resonance imaging(MRI) reconstruction, emphasizing their potential to overcome the limitations of supervised methods dependent on fully sampled k-space data. While DL has significantly advanced MRI, supervised approaches require large amounts of fully sampled k-space data for training-a major limitation given the impracticality and expense of acquiring such data clinically. Self-supervised learning has emerged as a promising alternative, enabling model training using only undersampled k-space data, thereby enhancing feasibility and driving research interest. We conducted a comprehensive literature review to synthesize recent progress in self-supervised DL for MRI reconstruction. The analysis focused on methods and architectures designed to improve image quality, reduce scanning time, and address data scarcity challenges, drawing from peer-reviewed publications and technical innovations in the field. Self-supervised DL holds transformative potential for MRI reconstruction, offering solutions to data limitations while maintaining image quality and accelerating scans. Key challenges include robustness across diverse anatomies, standardization of validation, and clinical integration. Future research should prioritize hybrid methodologies, domain-specific adaptations, and rigorous clinical validation. This review consolidates advancements and unresolved issues, providing a foundation for next-generation medical imaging technologies.

In recent years, deep learning has demonstrated great potential in accelerating Magnetic Resonance Imaging (MRI). However, most existing works simply consider MRI reconstruction as an image-to-image task, or typically use a single and identical network for both frequency and image domain reconstruction simultaneously, without taking into consideration the data characteristics and internal interactions of the two domains, which leads to ineffective learning of the image reconstruction models. In this study, we proposed an attention-based, dual-domain reconstruction network to facilitate fast and accurate MRI reconstruction by adaptively learning different data characteristics in the frequency domain and image domain. In response to the inhomogeneous energy distribution in K-space, we designed a densely connected multi-attention network for frequency domain reconstruction. For image aliasing at low sampling rates, we developed a residual encoder-decoder network with an attention module for the image domain reconstruction. The overall network contains two parallel and interactive branches that simultaneously perform on K-space and image data, with the data fusion modules to fuse dual domain information in each reconstruction layer, and the long skip connections to transfer inter-layer information. We have evaluated our method on two datasets. A series of comparative and ablation experiments demonstrate that our method effectively reconstructs images from undersampled K-space data, achieving better image reconstruction performance and restoring significant textures of brain slices.

Image reconstruction from undersampled k-space data accelerates magnetic resonance imaging (MRI) by exploiting image sparseness in certain transform domains. Employing image patch representation over a learned dictionary has the advantage of being adaptive to local image structures and thus can better sparsify images than using fixed transforms (e.g. wavelets and total variations). Dictionary learning methods have recently been introduced to MRI reconstruction, and these methods demonstrate significantly reduced reconstruction errors compared to sparse MRI reconstruction using fixed transforms. However, the synthesis sparse coding problem in dictionary learning is NP-hard and computationally expensive. In this paper, we present a novel sparsity-promoting orthogonal dictionary updating method for efficient image reconstruction from highly undersampled MRI data. The orthogonality imposed on the learned dictionary enables the minimization problem in the reconstruction to be solved by an efficient optimization algorithm which alternately updates representation coefficients, orthogonal dictionary, and missing k-space data. Moreover, both sparsity level and sparse representation contribution using updated dictionaries gradually increase during iterations to recover more details, assuming the progressively improved quality of the dictionary. Simulation and real data experimental results both demonstrate that the proposed method is approximately 10 to 100 times faster than the K-SVD-based dictionary learning MRI method and simultaneously improves reconstruction accuracy.

Purpose: To evaluate the feasibility of using the weighted hybrid iterative spiral k-space encoded estimation (WHISKEE) technique to improve spatial resolution of tracking images for onboard MR image guided radiation therapy (MR-IGRT). Methods: MR tracking images of abdomen and pelvis had been acquired from healthy volunteers using the ViewRay onboard MRIGRT system (ViewRay Inc. Oakwood Village, OH) at a spatial resolution of 2.0mm*2.0mm*5.0mm. The tracking MR images were acquired using the TrueFISP sequence. The temporal resolution had to be traded off to 2 frames per second (FPS) to achieve the 2.0mm in-plane spatial resolution. All MR images were imported into the MATLAB software. K-space data were synthesized through the Fourier Transform of the MR images. A mask was created to selected k-space points that corresponded to the under-sampled spiral k-space trajectory with an acceleration (or undersampling) factor of 3. The mask was applied to the fully sampled k-space data to synthesize the undersampled k-space data. The WHISKEE method was applied to the synthesized undersampled k-space data to reconstructed tracking MR images at 6 FPS. As a comparison, the undersampled k-space data were also reconstructed using the zero-padding technique. The reconstructed images were compared to the original image. The relatively reconstructionmore » error was evaluated using the percentage of the norm of the differential image over the norm of the original image. Results: Compared to the zero-padding technique, the WHISKEE method was able to reconstruct MR images with better image quality. It significantly reduced the relative reconstruction error from 39.5% to 3.1% for the pelvis image and from 41.5% to 4.6% for the abdomen image at an acceleration factor of 3. Conclusion: We demonstrated that it was possible to use the WHISKEE method to expedite MR image acquisition for onboard MR-IGRT systems to achieve good spatial and temporal resolutions simultaneously. Y. Hu and O. green receive travel reimbursement from ViewRay. S. Mutic has consulting and research agreements with ViewRay. Q. Zeng, R. Nana, J.L. Patrick, S. Shvartsman and J.F. Dempsey are ViewRay employees.« less

Coronary vessel wall magnetic resonance (MR) imaging is important for heart disease diagnosis but often suffers long scan time. Compressed sensing (CS) has been previously used to accelerate MR imaging by reconstructing an MR image from undersampled k-space data using a regularization framework. However, the widely used regularizations in the current CS methods often lead to smoothing effects and thus are unable to reconstruct the coronary vessel walls with sufficient resolution. To address this issue, a novel block-weighted total variation regularization is presented to accelerate the coronary vessel wall MR imaging. The proposed regularization divides the image into two parts: a region-of-interest (ROI) which contains the coronary vessel wall, and the other region with less concerned features. Different penalty weights are given to the two regions. As a result, the small details within ROI do not suffer from over-smoothing while the noise outside the ROI can be significantly suppressed. Results with both numerical simulations and in vivo experiments demonstrated that the proposed method can reconstruct the coronary vessel wall from undersampled k-space data with higher qualities than the conventional CS with the total variation or the edge-preserved total variation.

An approach to Magnetic Resonance (MR) image reconstruction from undersampled data is proposed. Undersampling artifacts are removed using an iterative thresholding algorithm applied to nonlinearly transformed image block arrays. Each block array is transformed using kernel principal component analysis where the contribution of each image block to the transform depends in a nonlinear fashion on the distance to other image blocks. Elimination of undersampling artifacts is achieved by conventional principal component analysis in the nonlinear transform domain, projection onto the main components and back-mapping into the image domain. Iterative image reconstruction is performed by interleaving the proposed undersampling artifact removal step and gradient updates enforcing consistency with acquired k-space data. The algorithm is evaluated using retrospectively undersampled MR cardiac cine data and compared to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT reconstruction. Evaluation of image quality and root-mean-squared-error (RMSE) reveal improved image reconstruction for up to 8-fold undersampled data with the proposed approach relative to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT. In conclusion, block matching and kernel methods can be used for effective removal of undersampling artifacts in MR image reconstruction and outperform methods using standard compressed sensing and ℓ1-regularized parallel imaging methods.

The application of compressed sensing (CS) to magnetic resonance (MR) images utilizes the transformed domain sparsity to enable the reconstruction from an under-sampled k-space (Fourier) data using a non-linear recovery algorithm. In order to estimate the missing k-space data from the partial Fourier samples, the reconstruction algorithms minimize an objective function based on mixed l1 − l2 norms. Iterative-shrinkage algorithms, such as parallel coordinate descent (PCD) and separable surrogate functional, provide an efficient numerical technique to minimize the l1-regularized least square optimization problem. These algorithms require a thresholding step to induce sparsity in the solution, which is an essential requirement of the CS recovery. This paper introduces a novel soft-thresholding method based on the hyperbolic tangent function. It has been shown that by using the proposed thresholding function in the sparsifying domain and a data consistency step in the k-space, the iterative-shrinkage algorithms can be used effectively to recover the under-sampled MR images. For the purpose of demonstration, we use the proposed soft-thresholding and data consistency with the PCD algorithm and compare its performance with the conventional PCD, projection onto convex sets and low-resolution reconstruction methods. The metrics used to compare the various algorithms are the artifact power, the peak signal-to-noise ratio, the correlation and the structural similarity index. The experimental results are validated using Shepp–Logan phantom image as well as real human head MR images taken from the MRI scanner at St. Mary’s Hospital, London.

With the successful application of deep learning to magnetic resonance (MR) imaging, parallel imaging techniques based on neural networks have attracted wide attention. However, in the absence of high-quality, fully sampled datasets for training, the performance of these methods is limited. And the interpretability of models is not strong enough. To tackle this issue, this paper proposes a Physics-bAsed unsupeRvised Contrastive rEpresentation Learning (PARCEL) method to speed up parallel MR imaging. Specifically, PARCEL has a parallel framework to contrastively learn two branches of model-based unrolling networks from augmented undersampled multi-coil k-space data. A sophisticated co-training loss with three essential components has been designed to guide the two networks in capturing the inherent features and representations for MR images. And the final MR image is reconstructed with the trained contrastive networks. PARCEL was evaluated on two vivo datasets and compared to five state-of-the-art methods. The results show that PARCEL is able to learn essential representations for accurate MR reconstruction without relying on fully sampled datasets. The code will be made available at https://github.com/ternencewu123/PARCEL.

This paper introduces an efficient algorithm for magnetic resonance (MR) image reconstruction. The proposed method minimizes a linear combination of nonlocal total variation and least-square data-fitting term to reconstruct the MR images from undersampled k-space data. The nonlocal total variation is taken as the L 1-regularization functional and solved using Split Bregman iteration. The proposed algorithm is compared with previous methods in terms of the reconstruction accuracy and computational complexity. The comparison results demonstrate the superiority of the proposed algorithm for compressed MR image reconstruction.