Undersampled MRI reconstruction with patch-based directional wavelets

An accelerated alternating direction method of multiplier for MRI with TV regularisation

Compressed Sensing (CS) is important in the field of image processing and signal processing, and CS-Magnetic Resonance Imaging (MRI) is used to reconstruct image from undersampled k-space data. Total Variation (TV) regularisation is a common technique to improve the sparsity of image, and the Alternating Direction Multiplier Method (ADMM) plays a key role in the variational image processing problem. This paper aims to improve the quality of MRI and shorten the reconstruction time. We consider MRI to solve a linear inverse problem, we convert it into a constrained optimization problem based on TV regularisation, then an accelerated ADMM is established. Through a series of theoretical derivations, we verify that the algorithm satisfies the convergence rate of O1/k2 under the condition that one objective function is quadratically convex and the other is strongly convex. We select five undersampled templates for testing in MRI experiment and compare it with other algorithms, experimental results show that our proposed method not only improves the running speed but also gives better reconstruction results.

Complex-valued image reconstruction for compressed sensing MRI using hierarchical constraint

In Magnetic Resonance Imaging (MRI), the sequential acquisition of raw complex-valued image data in Fourier space, also known as k-space, results in extended examination times. To speed up the MRI scans, k-space data are usually undersampled and processed using numerical techniques such as compressed sensing (CS). While the majority of CS-MRI algorithms primarily focus on magnitude images due to their significant diagnostic value, the phase components of complex-valued MRI images also hold substantial importance for clinical diagnosis, including neurodegenerative diseases. In this work, complex-valued MRI reconstruction is studied with a focus on the simultaneous reconstruction of both magnitude and phase images. The proposed algorithm is based on the nonsubsampled contourlet transform (NSCT) technique, which offers shift invariance in images. Instead of directly transforming the complex-valued image into the NSCT domain, we introduce a wavelet transform within the NSCT domain, reducing the size of the sparsity of coefficients. This two-level hierarchical constraint (HC) enforces sparse representation of complex-valued images for CS-MRI implementation. The proposed HC is seamlessly integrated into a proximal algorithm simultaneously. Additionally, to effectively minimize the artifacts caused by sub-sampling, thresholds related to different sub-bands in the HC are applied through an alternating optimization process. Experimental results show that the novel method outperforms existing CS-MRI techniques in phase-regularized complex-valued image reconstructions.

MRI reconstruction with enhanced self-similarity using graph convolutional network

BACKGROUND

Recent Convolutional Neural Networks (CNNs) perform low-error reconstruction in fast Magnetic Resonance Imaging (MRI). Most of them convolve the image with kernels and successfully explore the local information. Nonetheless, the non-local image information, which is embedded among image patches relatively far from each other, may be lost due to the limitation of the receptive field of the convolution kernel. We aim to incorporate a graph to represent non-local information and improve the reconstructed images by using the Graph Convolutional Enhanced Self-Similarity (GCESS) network.

METHODS

First, the image is reconstructed into the graph to extract the non-local self-similarity in the image. Second, GCESS uses spatial convolution and graph convolution to process the information in the image, so that local and non-local information can be effectively utilized. The network strengthens the non-local similarity between similar image patches while reconstructing images, making the reconstruction of structure more reliable.

RESULTS

Experimental results on in vivo knee and brain data demonstrate that the proposed method achieves better artifact suppression and detail preservation than state-of-the-art methods, both visually and quantitatively. Under 1D Cartesian sampling with 4 × acceleration (AF = 4), the PSNR of knee data reached 34.19 dB, 1.05 dB higher than that of the compared methods; the SSIM achieved 0.8994, 2% higher than the compared methods. Similar results were obtained for the reconstructed images under other sampling templates as demonstrated in our experiment.

CONCLUSIONS

The proposed method successfully constructs a hybrid graph convolution and spatial convolution network to reconstruct images. This method, through its training process, amplifies the non-local self-similarities, significantly benefiting the structural integrity of the reconstructed images. Experiments demonstrate that the proposed method outperforms the state-of-the-art reconstruction method in suppressing artifacts, as well as in preserving image details.

A convergence analysis for projected fast iterative soft-thresholding algorithm under radial sampling MRI

Radial sampling is a fast magnetic resonance imaging technique. Further imaging acceleration can be achieved with undersampling but how to reconstruct a clear image with fast algorithm is still challenging. Previous work has shown the advantage of removing undersampling image artifacts using the tight-frame sparse reconstruction model. This model was further solved with a projected fast iterative soft-thresholding algorithm (pFISTA). However, the convergence of this algorithm under radial sampling has not been clearly set up. In this work, the authors derived a theoretical convergence condition for this algorithm. This condition was approximated by estimating the maximal eigenvalue of reconstruction operators through the power iteration. Based on the condition, an optimal step size was further suggested to allow the fastest convergence. Verifications were made on the prospective in vivo data of static brain imaging and dynamic contrast-enhanced liver imaging, demonstrating that the recommended parameter allowed fast convergence in radial MRI.

Undersampled MRI reconstruction based on spectral graph wavelet transform

Compressed sensing magnetic resonance imaging (CS-MRI) has exhibited great potential to accelerate magnetic resonance imaging if an image can be sparsely represented. How to sparsify the image significantly affects the reconstruction quality of images. In this paper, a spectral graph wavelet transform (SGWT) is introduced to sparsely represent magnetic resonance images in iterative image reconstructions. The SGWT is achieved by extending the traditional wavelets transform to the signal defined on the vertices of the weighted graph, i.e. the spectral graph domain. This SGWT uses only the connectivity information encoded in the edge weights, and does not rely on any other attributes of the vertices. Therefore, SGWT can be defined and calculated for any domain where the underlying relations between data locations can be represented by a weighted graph. Furthermore, we present a Chebyshev polynomial approximation algorithm for fast computing this SGWT transform. The l₁ norm regularized CS-MRI reconstruction model is introduced and solved by the projected iterative soft-thresholding algorithm to verify its feasibility. Numerical experiment results demonstrate that our proposed method outperforms several state-of-the-art sparsify transforms in terms of suppressing artifacts and achieving lower reconstruction errors on the tested datasets.

DBGAN: A dual-branch generative adversarial network for undersampled MRI reconstruction

Compressed sensing magnetic resonance imaging (CS-MRI) greatly accelerates the acquisition process and yield considerable reconstructed images. Deep learning was introduced into CS-MRI to further speed up the reconstruction process and improve the image quality. Recently, generative adversarial network (GAN) using two-stage cascaded U-Net structure as generator has been proven to be effective in MRI reconstruction. However, previous cascaded structure was limited to few feature information propagation channels thus may lead to information missing. In this paper, we proposed a GAN-based model, DBGAN, for MRI reconstruction from undersampled k-space data. The model uses cross-stage skip connection (CSSC) between two end-to-end cascaded U-Net in our generator to widen the channels of feature propagation. To avoid discrepancy between training and inference, we replaced classical batch normalization (BN) with instance normalization (IN) . A stage loss is involved in the loss function to boost the training performance. In addition, a bilinear interpolation decoder branch is introduced in the generator to supplement the missing information of the deconvolution decoder. Tested under five variant patterns with four undersampling rates on different modality of MRI data, the quantitative results show that DBGAN model achieves mean improvements of 3.65 dB in peak signal-to-noise ratio (PSNR) and 0.016 in normalized mean square error (NMSE) compared with state-of-the-art GAN-based methods on T1-Weighted brain dataset from MICCAI 2013 grand challenge. The qualitative visual results show that our method can reconstruct considerable images on brain and knee MRI data from different modality. Furthermore, DBGAN is light and fast - the model parameters are fewer than half of state-of-the-art GAN-based methods and each 256 × 256 image is reconstructed in 60 milliseconds, which is suitable for real-time processing.

Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data

The discrete shearlet transformation accurately represents the discontinuities and edges occurring in magnetic resonance imaging, providing an excellent option of a sparsifying transform. In the present paper, we examine the use of discrete shearlets over other sparsifying transforms in a low-rank plus sparse decomposition problem, denoted by L+S. The proposed algorithm is evaluated on simulated dynamic contrast enhanced (DCE) and small bowel data. For the small bowel, eight subjects were scanned; the sequence was run first on breath-holding and subsequently on free-breathing, without changing the anatomical position of the subject. The reconstruction performance of the proposed algorithm was evaluated against k-t FOCUSS. L+S decomposition, using discrete shearlets as sparsifying transforms, successfully separated the low-rank (background and periodic motion) from the sparse component (enhancement or bowel motility) for both DCE and small bowel data. Motion estimated from low-rank of DCE data is closer to ground truth deformations than motion estimated from L and S. Motility metrics derived from the S component of free-breathing data were not significantly different from the ones from breath-holding data up to four-fold undersampling, indicating that bowel (rapid/random) motility is isolated in S. Our work strongly supports the use of discrete shearlets as a sparsifying transform in a L+S decomposition for undersampled MR data.

Task-Oriented Convex Bilevel Optimization With Latent Feasibility

This paper firstly proposes a convex bilevel optimization paradigm to formulate and optimize popular learning and vision problems in real-world scenarios. Different from conventional approaches, which directly design their iteration schemes based on given problem formulation, we introduce a task-oriented energy as our latent constraint which integrates richer task information. By explicitly re- characterizing the feasibility, we establish an efficient and flexible algorithmic framework to tackle convex models with both shrunken solution space and powerful auxiliary (based on domain knowledge and data distribution of the task). In theory, we present the convergence analysis of our latent feasibility re- characterization based numerical strategy. We also analyze the stability of the theoretical convergence under computational error perturbation. Extensive numerical experiments are conducted to verify our theoretical findings and evaluate the practical performance of our method on different applications.

A review on deep learning MRI reconstruction without fully sampled k-space

BACKGROUND

Magnetic resonance imaging (MRI) is an effective auxiliary diagnostic method in clinical medicine, but it has always suffered from the problem of long acquisition time. Compressed sensing and parallel imaging are two common techniques to accelerate MRI reconstruction. Recently, deep learning provides a new direction for MRI, while most of them require a large number of data pairs for training. However, there are many scenarios where fully sampled k-space data cannot be obtained, which will seriously hinder the application of supervised learning. Therefore, deep learning without fully sampled data is indispensable.

MAIN TEXT

In this review, we first introduce the forward model of MRI as a classic inverse problem, and briefly discuss the connection of traditional iterative methods to deep learning. Next, we will explain how to train reconstruction network without fully sampled data from the perspective of obtaining prior information.

CONCLUSION

Although the reviewed methods are used for MRI reconstruction, they can also be extended to other areas where ground-truth is not available. Furthermore, we may anticipate that the combination of traditional methods and deep learning will produce better reconstruction results.

Review and Prospect: Artificial Intelligence in Advanced Medical Imaging

Artificial intelligence (AI) as an emerging technology is gaining momentum in medical imaging. Recently, deep learning-based AI techniques have been actively investigated in medical imaging, and its potential applications range from data acquisition and image reconstruction to image analysis and understanding. In this review, we focus on the use of deep learning in image reconstruction for advanced medical imaging modalities including magnetic resonance imaging (MRI), computed tomography (CT), and positron emission tomography (PET). Particularly, recent deep learning-based methods for image reconstruction will be emphasized, in accordance with their methodology designs and performances in handling volumetric imaging data. It is expected that this review can help relevant researchers understand how to adapt AI for medical imaging and which advantages can be achieved with the assistance of AI.

Homotopic Gradients of Generative Density Priors for MR Image Reconstruction

Deep learning, particularly the generative model, has demonstrated tremendous potential to significantly speed up image reconstruction with reduced measurements recently. Rather than the existing generative models that often optimize the density priors, in this work, by taking advantage of the denoising score matching, homotopic gradients of generative density priors (HGGDP) are exploited for magnetic resonance imaging (MRI) reconstruction. More precisely, to tackle the low-dimensional manifold and low data density region issues in generative density prior, we estimate the target gradients in higher-dimensional space. We train a more powerful noise conditional score network by forming high-dimensional tensor as the network input at the training phase. More artificial noise is also injected in the embedding space. At the reconstruction stage, a homotopy method is employed to pursue the density prior, such as to boost the reconstruction performance. Experiment results implied the remarkable performance of HGGDP in terms of high reconstruction accuracy. Only 10% of the k-space data can still generate image of high quality as effectively as standard MRI reconstructions with the fully sampled data.

Investigating Customization Strategies and Convergence Behaviors of Task-Specific ADMM

Alternating Direction Method of Multiplier (ADMM) has been a popular algorithmic framework for separable optimization problems with linear constraints. For numerical ADMM fail to exploit the particular structure of the problem at hand nor the input data information, leveraging task-specific modules (e.g., neural networks and other data-driven architectures) to extend ADMM is a significant but challenging task. This work focuses on designing a flexible algorithmic framework to incorporate various task-specific modules (with no additional constraints) to improve the performance of ADMM in real-world applications. Specifically, we propose Guidance from Optimality (GO), a new customization strategy, to embed task-specific modules into ADMM (GO-ADMM). By introducing an optimality-based criterion to guide the propagation, GO-ADMM establishes an updating scheme agnostic to the choice of additional modules. The existing task-specific methods just plug their task-specific modules into the numerical iterations in a straightforward manner. Even with some restrictive constraints on the plug-in modules, they can only obtain some relatively weaker convergence properties for the resulted ADMM iterations. Fortunately, without any restrictions on the embedded modules, we prove the convergence of GO-ADMM regarding objective values and constraint violations, and derive the worst-case convergence rate measured by iteration complexity. Extensive experiments are conducted to verify the theoretical results and demonstrate the efficiency of GO-ADMM.

Synergistic multi-contrast cardiac magnetic resonance image reconstruction

Cardiac magnetic resonance imaging (CMR) is an important tool for the non-invasive diagnosis of a variety of cardiovascular diseases. Parametric mapping with multi-contrast CMR is able to quantify tissue alterations in myocardial disease and promises to improve patient care. However, magnetic resonance imaging is an inherently slow imaging modality, resulting in long acquisition times for parametric mapping which acquires a series of cardiac images with different contrasts for signal fitting or dictionary matching. Furthermore, extra efforts to deal with respiratory and cardiac motion by triggering and gating further increase the scan time. Several techniques have been developed to speed up CMR acquisitions, which usually acquire less data than that required by the Nyquist-Shannon sampling theorem, followed by regularized reconstruction to mitigate undersampling artefacts. Recent advances in CMR parametric mapping speed up CMR by synergistically exploiting spatial-temporal and contrast redundancies. In this article, we will review the recent developments in multi-contrast CMR image reconstruction for parametric mapping with special focus on low-rank and model-based reconstructions. Deep learning-based multi-contrast reconstruction has recently been proposed in other magnetic resonance applications. These developments will be covered to introduce the general methodology. Current technical limitations and potential future directions are discussed. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Spatiotemporal Flexible Sparse Reconstruction for Rapid Dynamic Contrast-enhanced MRI

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a tissue perfusion imaging technique. Some versatile free-breathing DCE-MRI techniques combining compressed sensing (CS) and parallel imaging with golden-angle radial sampling have been developed to improve motion robustness with high spatial and temporal resolution. These methods have demonstrated good diagnostic performance in clinical setting, but the reconstruction quality will degrade at high acceleration rates and overall reconstruction time remains long. In this paper, we proposed a new parallel CS reconstruction model for DCE-MRI that enforces flexible weighted sparse constraint along both spatial and temporal dimensions. Weights were introduced to flexibly adjust the importance of time and space sparsity, and we derived a fast-thresholding algorithm which was proven to be simple and efficient for solving the proposed reconstruction model. Results on both the brain tumor DCE and liver DCE show that, at relatively high acceleration factor of fast sampling, lowest reconstruction error and highest image structural similarity are obtained by the proposed method. Besides, the proposed method achieves faster reconstruction for liver datasets and better physiological measures are also obtained on tumor images.

A dual-task dual-domain model for blind MRI reconstruction

MRI reconstruction is the key technology to accelerate MR acquisition. Recent cascade models have gained satisfactory results, however, they deeply rely on the known sample mask, which we call it mask prior. To restore the MR image without mask prior, we designed an auxiliary network to estimate the mask from sampled k-space data. Experimentally, the sample mask can be completely estimated by the proposed network and be used to input to the cascade models. Moreover, we rethink the MRI reconstruction model as a k-space inpainting task. A dual-domain cascade network, which utilized partial convolutional layers to inpaint features in k-space, was presented to restore the MR image. Without the mask prior, our blind reconstruction model demonstrates the best reconstruction ability in both 4x acceleration and 8x acceleration.

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.

A guaranteed convergence analysis for the projected fast iterative soft-thresholding algorithm in parallel MRI

Sparse sampling and parallel imaging techniques are two effective approaches to alleviate the lengthy magnetic resonance imaging (MRI) data acquisition problem. Promising data recoveries can be obtained from a few MRI samples with the help of sparse reconstruction models. To solve the optimization models, proper algorithms are indispensable. The pFISTA, a simple and efficient algorithm, has been successfully extended to parallel imaging. However, its convergence criterion is still an open question. Besides, the existing convergence criterion of single-coil pFISTA cannot be applied to the parallel imaging pFISTA, which, therefore, imposes confusions and difficulties on users about determining the only parameter - step size. In this work, we provide the guaranteed convergence analysis of the parallel imaging version pFISTA to solve the two well-known parallel imaging reconstruction models, SENSE and SPIRiT. Along with the convergence analysis, we provide recommended step size values for SENSE and SPIRiT reconstructions to obtain fast and promising reconstructions. Experiments on in vivo brain images demonstrate the validity of the convergence criterion.

Reference-Driven Undersampled MR Image Reconstruction Using Wavelet Sparsity-Constrained Deep Image Prior

Deep learning has shown potential in significantly improving performance for undersampled magnetic resonance (MR) image reconstruction. However, one challenge for the application of deep learning to clinical scenarios is the requirement of large, high-quality patient-based datasets for network training. In this paper, we propose a novel deep learning-based method for undersampled MR image reconstruction that does not require pre-training procedure and pre-training datasets. The proposed reference-driven method using wavelet sparsity-constrained deep image prior (RWS-DIP) is based on the DIP framework and thereby reduces the dependence on datasets. Moreover, RWS-DIP explores and introduces structure and sparsity priors into network learning to improve the efficiency of learning. By employing a high-resolution reference image as the network input, RWS-DIP incorporates structural information into network. RWS-DIP also uses the wavelet sparsity to further enrich the implicit regularization of traditional DIP by formulating the training of network parameters as a constrained optimization problem, which is solved using the alternating direction method of multipliers (ADMM) algorithm. Experiments on in vivo MR scans have demonstrated that the RWS-DIP method can reconstruct MR images more accurately and preserve features and textures from undersampled k-space measurements.

High quality and fast compressed sensing MRI reconstruction via edge-enhanced dual discriminator generative adversarial network

Generative adversarial networks (GAN) are widely used for fast compressed sensing magnetic resonance imaging (CSMRI) reconstruction. However, most existing methods are difficult to make an effective trade-off between abstract global high-level features and edge features. It easily causes problems, such as significant remaining aliasing artifacts and clearly over-smoothed reconstruction details. To tackle these issues, we propose a novel edge-enhanced dual discriminator generative adversarial network architecture called EDDGAN for CSMRI reconstruction with high quality. In this model, we extract effective edge features by fusing edge information from different depths. Then, leveraging the relationship between abstract global high-level features and edge features, a three-player game is introduced to control the hallucination of details and stabilize the training process. The resulting EDDGAN can offer more focus on edge restoration and de-aliasing. Extensive experimental results demonstrate that our method consistently outperforms state-of-the-art methods and obtains reconstructed images with rich edge details. In addition, our method also shows remarkable generalization, and its time consumption for each 256 × 256 image reconstruction is approximately 8.39 ms.

Spatial orthogonal attention generative adversarial network for MRI reconstruction

PURPOSE

Recent studies have witnessed that self-attention modules can better solve the vision understanding problems by capturing long-range dependencies. However, there are very few works designing a lightweight self-attention module to improve the quality of MRI reconstruction. Furthermore, it can be observed that several important self-attention modules (e.g., the non-local block) cause high computational complexity and need a huge number of GPU memory when the size of the input feature is large. The purpose of this study is to design a lightweight yet effective spatial orthogonal attention module (SOAM) to capture long-range dependencies, and develop a novel spatial orthogonal attention generative adversarial network, termed as SOGAN, to achieve more accurate MRI reconstruction.

METHODS

We first develop a lightweight SOAM, which can generate two small attention maps to effectively aggregate the long-range contextual information in vertical and horizontal directions, respectively. Then, we embed the proposed SOAMs into the concatenated convolutional autoencoders to form the generator of the proposed SOGAN.

RESULTS

The experimental results demonstrate that the proposed SOAMs improve the quality of the reconstructed MR images effectively by capturing long-range dependencies. Besides, compared with state-of-the-art deep learning-based CS-MRI methods, the proposed SOGAN reconstructs MR images more accurately, but with fewer model parameters.

CONCLUSIONS

The proposed SOAM is a lightweight yet effective self-attention module to capture long-range dependencies, thus, can improve the quality of MRI reconstruction to a large extent. Besides, with the help of SOAMs, the proposed SOGAN outperforms the state-of-the-art deep learning-based CS-MRI methods.

A Deep Framework Assembling Principled Modules for CS-MRI: Unrolling Perspective, Convergence Behaviors, and Practical Modeling

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) significantly accelerates MR acquisition at a sampling rate much lower than the Nyquist criterion. A major challenge for CS-MRI lies in solving the severely ill-posed inverse problem to reconstruct aliasing-free MR images from the sparse k -space data. Conventional methods typically optimize an energy function, producing restoration of high quality, but their iterative numerical solvers unavoidably bring extremely large time consumption. Recent deep techniques provide fast restoration by either learning direct prediction to final reconstruction or plugging learned modules into the energy optimizer. Nevertheless, these data-driven predictors cannot guarantee the reconstruction following principled constraints underlying the domain knowledge so that the reliability of their reconstruction process is questionable. In this paper, we propose a deep framework assembling principled modules for CS-MRI that fuses learning strategy with the iterative solver of a conventional reconstruction energy. This framework embeds an optimal condition checking mechanism, fostering efficient and reliable reconstruction. We also apply the framework to three practical tasks, i.e., complex-valued data reconstruction, parallel imaging and reconstruction with Rician noise. Extensive experiments on both benchmark and manufacturer-testing images demonstrate that the proposed method reliably converges to the optimal solution more efficiently and accurately than the state-of-the-art in various scenarios.

Deep Convolutional Encoder-Decoder algorithm for MRI brain reconstruction

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) could be considered a challenged task since it could be designed as an efficient technique for fast MRI acquisition which could be highly beneficial for several clinical routines. In fact, it could grant better scan quality by reducing motion artifacts amount as well as the contrast washout effect. It offers also the possibility to reduce the exploration cost and the patient's anxiety. Recently, Deep Learning Neuronal Network (DL) has been suggested in order to reconstruct MRI scans with conserving the structural details and improving parallel imaging-based fast MRI. In this paper, we propose Deep Convolutional Encoder-Decoder architecture for CS-MRI reconstruction. Such architecture bridges the gap between the non-learning techniques, using data from only one image, and approaches using large training data. The proposed approach is based on autoencoder architecture divided into two parts: an encoder and a decoder. The encoder as well as the decoder has essentially three convolutional blocks. The proposed architecture has been evaluated through two databases: Hammersmith dataset (for the normal scans) and MICCAI 2018 (for pathological MRI). Moreover, we extend our model to cope with noisy pathological MRI scans. The normalized mean square error (NMSE), the peak-to-noise ratio (PSNR), and the structural similarity index (SSIM) have been adopted as evaluation metrics in order to evaluate the proposed architecture performance and to make a comparative study with the state-of-the-art reconstruction algorithms. The higher PSNR and SSIM values as well as the lowest NMSE values could attest that the proposed architecture offers better reconstruction and preserves textural image details. Furthermore, the running time is about 0.8 s, which is suitable for real-time processing. Such results could encourage the neurologist to adopt it in their clinical routines. Graphical abstract.

Triple-D network for efficient undersampled magnetic resonance images reconstruction

Compressed sensing (CS) theory can help accelerate magnetic resonance imaging (MRI) by sampling partial k-space measurements. However, conventional optimization-based CS-MRI methods are often time-consuming and are based on fixed transform or shallow image dictionaries, which limits modeling capabilities. Recently, deep learning models have been used to solve the CS-MRI problem. However, recent researches have focused on modeling in image domain, and the potential of k-space modeling capability has not been utilized seriously. In this paper, we propose a deep model called Dual Domain Dense network (Triple-D network), which consisted of some k-space and image domain sub-network. These sub-networks are connected with dense connections, which can utilize feature maps at different levels to enhance performance. To further promote model capabilities, we use two strategies: multi-supervision strategies, which can avoid loss of supervision information; channel-wise attention layer (CA layer), which can adaptively adjust the weight of the feature map. Experimental results show that the proposed Triple-D network provides promising performance in CS-MRI, and it can effectively work on different sampling trajectories and noisy settings.

Dense Recurrent Neural Networks for Accelerated MRI: History-Cognizant Unrolling of Optimization Algorithms

Inverse problems for accelerated MRI typically incorporate domain-specific knowledge about the forward encoding operator in a regularized reconstruction framework. Recently physics-driven deep learning (DL) methods have been proposed to use neural networks for data-driven regularization. These methods unroll iterative optimization algorithms to solve the inverse problem objective function, by alternating between domain-specific data consistency and data-driven regularization via neural networks. The whole unrolled network is then trained end-to-end to learn the parameters of the network. Due to simplicity of data consistency updates with gradient descent steps, proximal gradient descent (PGD) is a common approach to unroll physics-driven DL reconstruction methods. However, PGD methods have slow convergence rates, necessitating a higher number of unrolled iterations, leading to memory issues in training and slower reconstruction times in testing. Inspired by efficient variants of PGD methods that use a history of the previous iterates, we propose a history-cognizant unrolling of the optimization algorithm with dense connections across iterations for improved performance. In our approach, the gradient descent steps are calculated at a trainable combination of the outputs of all the previous regularization units. We also apply this idea to unrolling variable splitting methods with quadratic relaxation. Our results in reconstruction of the fastMRI knee dataset show that the proposed history-cognizant approach reduces residual aliasing artifacts compared to its conventional unrolled counterpart without requiring extra computational power or increasing reconstruction time.

Compressed sensing MRI using an interpolation-free nonlinear diffusion model

PURPOSE

Constraints in extended neighborhood system demand the use of a large number of interpolations in directionality-guided compressed-sensing nonlinear diffusion MR image reconstruction technique. This limits its practical application in terms of computational complexity. The proposed method aims at multifold improvement in its runtime without compromising the image quality.

THEORY AND METHODS

Conventional approach to extended neighborhood computation requires 108 linear interpolations per pixel for 10 sets of neighborhoods. We propose a neighborhood stretching technique that systematically extends the location of neighboring pixels such that 66% to 100% fewer interpolations are required to compute the gradients along multiple directions. A spatial frequency-based deviation measure is then used to choose the most reliable edges from the set of images generated by diffusion along different directions.

RESULTS

The semi-interpolated and interpolation-free diffusion techniques proposed in this paper are compared with the fully interpolated diffusion-based reconstruction by reconstruing multiple multichannel in vivo datasets, undersampled using different sampling patterns at various sampling rates. Results indicate a two- to fivefold increase in reconstruction speed with a potential to generate 1 to 2 dB improvement in peak SNR measure.

CONCLUSION

The proposed method outperforms the state-of-the-art fully interpolated diffusion model and generates high-quality reconstructions for different sampling patterns and acceleration factors with a two- to fivefold increment in reconstruction speed. This makes it the most suitable candidate for edge-preserving penalties used in the compressed sensing MRI reconstruction methods.

pFISTA-SENSE-ResNet for parallel MRI reconstruction

Magnetic resonance imaging has been widely applied in clinical diagnosis. However, it is limited by its long data acquisition time. Although the imaging can be accelerated by sparse sampling and parallel imaging, achieving promising reconstructed images with a fast computation speed remains a challenge. Recently, deep learning methods have attracted a lot of attention for encouraging reconstruction results, but they are lack of proper interpretability for neural networks. In this work, in order to enable high-quality image reconstruction for the parallel magnetic resonance imaging, we design the network structure from the perspective of sparse iterative reconstruction and enhance it with the residual structure. Experimental results on a public knee dataset indicate that, as compared with the state-of-the-art deep learning-based and optimization-based methods, the proposed network achieves lower error in reconstruction and is more robust under different samplings.

High-dimensional embedding network derived prior for compressive sensing MRI reconstruction

Although recent deep learning methodology has shown promising performance in fast imaging, the network needs to be retrained for specific sampling patterns and ratios. Therefore, how to explore the network as a general prior and leverage it into the observation constraint flexibly is urgent. In this work, we present a multi-channel enhanced Deep Mean-Shift Prior (MEDMSP) to address the highly under-sampled magnetic resonance imaging reconstruction problem. By extending the naive DMSP via integration of multi-model aggregation and multi-channel network learning, a high-dimensional embedding network derived prior is formed. Then, we apply the learned prior to single-channel image reconstruction via variable augmentation technique. The resulting model is tackled by proximal gradient descent and alternative iteration. Experimental results under various sampling trajectories and acceleration factors consistently demonstrated the superiority of the proposed prior.

Compressed MRI reconstruction exploiting a rotation-invariant total variation discretization

Inspired by the first-order method of Malitsky and Pock, we propose a new variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. In the first step, we provide theoretical and numerical analysis establishing the exceptional rotation-invariance property of this total variation functional and observe its superiority over other well-known variational regularization terms in both upright and rotated imaging setups. Thereupon, the proposed MRI reconstruction model is presented as a constrained optimization problem, however, we do not use conventional ADMM-type algorithms designed for constrained problems to obtain a solution, but rather we tailor the linesearch-equipped method of Malitsky and Pock to our model, which was originally proposed for unconstrained problems. As attested by numerical experiments, this framework significantly outperforms various state-of-the-art algorithms from variational methods to adaptive and learning approaches and in particular, it eliminates the stagnating behavior of a previous work on BM3D-MRI which compromised the solution beyond a certain iteration.

Coupled Dictionary Learning for Multi-Contrast MRI Reconstruction

Magnetic resonance (MR) imaging tasks often involve multiple contrasts, such as T1-weighted, T2-weighted and fluid-attenuated inversion recovery (FLAIR) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities in either structure level or gray level. In this paper, we propose a coupled dictionary learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage the dependency correlation between different contrasts for guided or joint reconstruction from their under-sampled k -space data. Our approach iterates between three stages: coupled dictionary learning, coupled sparse denoising, and enforcing k -space consistency. The first stage learns a set of dictionaries that not only are adaptive to the contrasts, but also capture correlations among multiple contrasts in a sparse transform domain. By capitalizing on the learned dictionaries, the second stage performs coupled sparse coding to remove the aliasing and noise in the corrupted contrasts. The third stage enforces consistency between the denoised contrasts and the measurements in the k -space domain. Numerical experiments, consisting of retrospective under-sampling of various MRI contrasts with a variety of sampling schemes, demonstrate that CDLMRI is capable of capturing structural dependencies between different contrasts. The learned priors indicate notable advantages in multi-contrast MR imaging and promising applications in quantitative MR imaging such as MR fingerprinting.

ADMM-CSNet: A Deep Learning Approach for Image Compressive Sensing

Compressive sensing (CS) is an effective technique for reconstructing image from a small amount of sampled data. It has been widely applied in medical imaging, remote sensing, image compression, etc. In this paper, we propose two versions of a novel deep learning architecture, dubbed as ADMM-CSNet, by combining the traditional model-based CS method and data-driven deep learning method for image reconstruction from sparsely sampled measurements. We first consider a generalized CS model for image reconstruction with undetermined regularizations in undetermined transform domains, and then two efficient solvers using Alternating Direction Method of Multipliers (ADMM) algorithm for optimizing the model are proposed. We further unroll and generalize the ADMM algorithm to be two deep architectures, in which all parameters of the CS model and the ADMM algorithm are discriminatively learned by end-to-end training. For both applications of fast CS complex-valued MR imaging and CS imaging of real-valued natural images, the proposed ADMM-CSNet achieved favorable reconstruction accuracy in fast computational speed compared with the traditional and the other deep learning methods.

A deep error correction network for compressed sensing MRI

BACKGROUND

CS-MRI (compressed sensing for magnetic resonance imaging) exploits image sparsity properties to reconstruct MRI from very few Fourier k-space measurements. Due to imperfect modelings in the inverse imaging, state-of-the-art CS-MRI methods tend to leave structural reconstruction errors. Compensating such errors in the reconstruction could help further improve the reconstruction quality.

RESULTS

In this work, we propose a DECN (deep error correction network) for CS-MRI. The DECN model consists of three parts, which we refer to as modules: a guide, or template, module, an error correction module, and a data fidelity module. Existing CS-MRI algorithms can serve as the template module for guiding the reconstruction. Using this template as a guide, the error correction module learns a CNN (convolutional neural network) to map the k-space data in a way that adjusts for the reconstruction error of the template image. We propose a deep error correction network. Our experimental results show the proposed DECN CS-MRI reconstruction framework can considerably improve upon existing inversion algorithms by supplementing with an error-correcting CNN.

CONCLUSIONS

In the proposed a deep error correction framework, any off-the-shelf CS-MRI algorithm can be used as template generation. Then a deep neural network is used to compensate reconstruction errors. The promising experimental results validate the effectiveness and utility of the proposed framework.

Efficient directionality-driven dictionary learning for compressive sensing magnetic resonance imaging reconstruction

Compressed sensing is an acquisition strategy that possesses great potential to accelerate magnetic resonance imaging (MRI) within the ambit of existing hardware, by enforcing sparsity on MR image slices. Compared to traditional reconstruction methods, dictionary learning-based reconstruction algorithms, which locally sparsify image patches, have been found to boost the reconstruction quality. However, due to the learning complexity, they have to be independently employed on successive MR undersampled slices one at a time. This causes them to forfeit prior knowledge of the anatomical structure of the region of interest. An MR reconstruction algorithm is proposed that employs the double sparsity model coupled with online sparse dictionary learning to learn directional features of the region under observation from existing prior knowledge. This is found to enhance the capability of sparsely representing directional features in an MR image and results in better reconstructions. The proposed framework is shown to have superior performance compared to state-of-art MRI reconstruction algorithms under noiseless and noisy conditions for various undersampling percentages and distinct scanning strategies.

Reference-Driven Compressed Sensing MR Image Reconstruction Using Deep Convolutional Neural Networks without Pre-Training

Deep learning has proven itself to be able to reduce the scanning time of Magnetic Resonance Imaging (MRI) and to improve the image reconstruction quality since it was introduced into Compressed Sensing MRI (CS-MRI). However, the requirement of using large, high-quality, and patient-based datasets for network training procedures is always a challenge in clinical applications. In this paper, we propose a novel deep learning based compressed sensing MR image reconstruction method that does not require any pre-training procedure or training dataset, thereby largely reducing clinician dependence on patient-based datasets. The proposed method is based on the Deep Image Prior (DIP) framework and uses a high-resolution reference MR image as the input of the convolutional neural network in order to induce the structural prior in the learning procedure. This reference-driven strategy improves the efficiency and effect of network learning. We then add the k-space data correction step to enforce the consistency of the k-space data with the measurements, which further improve the image reconstruction accuracy. Experiments on in vivo MR datasets showed that the proposed method can achieve more accurate reconstruction results from undersampled k-space data.