Compressed sensing MRI via fast linearized preconditioned alternating direction method of multipliers

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.

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

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.

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.

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)

To present and validate a manifold learning (ML)-based method that estimates the respiratory signal directly from undersampled k-space data and that can be applied for respiratory self-gated liver MRI. ML methods embed high-dimensional space data in a low-dimensional space while preserving their characteristic properties. These methods have been used to estimate one-dimensional respiratory motion (low-dimensional manifold) from a set of high-dimensional free-breathing abdominal MR images. These approaches require MR images to be reconstructed first from the acquired undersampled data. Recently, the concept of compressive manifold learning (CML) has been introduced that combines compressed sensing with ML by learning low-dimensional manifolds directly from a partial set of compressed measurements, provided that the sampling satisfies the restricted isometry property. We propose to use the CML concept to extract the respiratory signal directly from undersampled k-space data. Simulation results from free-breathing abdominal MR data show that CML can accurately estimate respiratory motion from highly retrospectively undersampled k-space (up to 25-fold acceleration under ideal assumptions). Prospective free-breathing golden-angle radial two-dimensional (2D) acquisitions further demonstrate the feasibility of the CML method for respiratory self-gating acquisition, estimating the respiratory motion from up to 15-fold accelerated MR data. The proposed method performs accurate respiratory signal estimation from highly undersampled k-space data and can be used for respiratory self-navigated 2D liver MRI.

Total variation (TV) regularization can very well remove noise and simultaneously preserve the sharp edges. But it has the drawback of the contrast loss in the restoration. In this paper, we first theoretically analyze the loss of contrast in the original TV regularization model, and then propose a forward-backward diffusion model in the framework of total variation, which can effectively preserve the edges and contrast in TV image denoising. A backward diffusion term based on a nonconvex and monotony decrease potential function is introduced in the TV energy, resulting in a forward-backward diffusion. In order to finely control the strength of the forward and backward diffusion, and separately design the efficient algorithm to numerically implement the forward and backward diffusion, we propose a two-step splitting method to iteratively solve the proposed model. We adopt the efficient projection algorithm in the dual framework to solve the forward diffusion in the first step, and then use the simple finite differences scheme to solve the backward diffusion to compensate the loss of contrast occurred in the previous step. At last, we test the models on both synthetic and real images. Compared with the classical TV, forward and backward diffusion (FBD), two-step methods (TSM), and TV-FF models, our model has the better performance in terms of peak signal-to-noise ratio (PSNR) and mean structural similarity (MSSIM) indexes.

Accelerated magnetic resonance imaging techniques reduce signal acquisition time by undersampling k-space. A fundamental problem in accelerated magnetic resonance imaging is the recovery of quality images from undersampled k-space data. Current state-of-the-art recovery algorithms exploit the spatial and temporal structures in underlying images to improve the reconstruction quality. In recent years, compressed sensing theory has helped formulate mathematical principles and conditions that ensure recovery of (structured) sparse signals from undersampled, incoherent measurements. In this article, a new recovery algorithm, motion-adaptive spatio-temporal regularization, is presented that uses spatial and temporal structured sparsity of MR images in the compressed sensing framework to recover dynamic MR images from highly undersampled k-space data. In contrast to existing algorithms, our proposed algorithm models temporal sparsity using motion-adaptive linear transformations between neighboring images. The efficiency of motion-adaptive spatio-temporal regularization is demonstrated with experiments on cardiac magnetic resonance imaging for a range of reduction factors. Results are also compared with k-t FOCUSS with motion estimation and compensation-another recently proposed recovery algorithm for dynamic magnetic resonance imaging. .

Reconstruction of an image from undersampled k-space data using conventional sparsity priors use any of the pre-specified transforms like wavelet, which utilizes the global sparsity of images. Alternatively, methods such as block-matching and 3D filtering (BM3D) utilize the non-local sparsity of images, resulting in better preservation of finer details. However, use of either of the methods cannot utilize global and non-local sparsity at the same time. In this paper, we propose an efficient combination of the global and non-local sparsity realized using wavelet and BM3D, implemented using the fast composite splitting denoising (FCSD) algorithm. Furthermore, we use an adaptive regularization parameter for the wavelet to yield the best achievable performance using adaptive thresholded Landweber (ATL). The proposed adaptive fast composite splitting denoising algorithm (AFCSD) combines the advantages of both BM3D with adaptive TL through the use of FCSD and thus exploits the self-repetitive structure in images by enforcing non-local sparsity as well as entire consistency of the image. Experimental results reveal that the proposed method is superior to any of the individual methods in terms of reconstruction accuracy and computation complexity. Additionally, when used as an auxiliary constraint in dictionary learning (DL), this can result in further improvements in reconstruction with significant reduction in the computation time as compared to a conventional DL reconstruction.

This paper introduced a novel method to reconstruct low-dose computed tomography (LDCT) images based on weighted total variation minimization. Previous work has shown that a CT image can be reconstructed from under-sampling data by minimizing the total variation (TV) of the image with some constraints. However, due to the piecewise constant assumption, the conventional TV minimization algorithm often suffers over-smooth on the edges of the resulted image. Considering the anisotropic property of the edge voxels in an image, we proposed a weighted total variation (WTV) minimization algorithm to achieve high-quality LDCT image reconstruction from under-sampling sinogram data. The proposed algorithm was evaluated by computer simulation, where the Shepp-Logan phantom was used. In noise free cases, 20 projection views were enough to accurately reconstruct the phantom image by the WTV approach while the filtered backprojection (FBP) reconstruction failed. In noise cases, different levels of Poisson noise were added to the noise-free sinogram. The local signal to noise ratio (SNR) and global SNR were computed to evaluate the robustness of the WTV algorithm to the noise. The simulation results showed that the WTV algorithm can have much higher global SNR compared to the conventional TV. The relationship between the number of views of WTV algorithm and the mean square error (MSE) of the reconstructed images was also discussed in this paper in order to find the minimum projection numbers required to obtain an adequate reconstruction image for low-dose CT applications.

Accelerating the acquisition of magnetic resonance imaging (MRI) is a challenging problem, and many works have been proposed to reconstruct images from undersampled k-space data. However, if the main purpose is to extract certain quantitative measures from the images, perfect reconstructions may not always be necessary as long as the images enable the means of extracting the clinically relevant measures. In this paper, we work on jointly predicting cardiac motion estimation and segmentation directly from undersampled data, which are two important steps in quantitatively assessing cardiac function and diagnosing cardiovascular diseases. In particular, a unified model consisting of both motion estimation branch and segmentation branch is learned by optimising the two tasks simultaneously. Additional corresponding fully-sampled images are incorporated into the network as a parallel sub-network to enhance and guide the learning during the training process. Experimental results using cardiac MR images from 220 subjects show that the proposed model is robust to undersampled data and is capable of predicting results that are close to that from fully-sampled ones, while bypassing the usual image reconstruction stage.

Parallel MRI techniques reconstruct full-FOV images from undersampled k-space data by using the uncorrelated information from RF array coil elements. One disadvantage of parallel MRI is that the image signal-to-noise ratio (SNR) is degraded because of the reduced data samples and the spatially correlated nature of multiple RF receivers. Regularization has been proposed to mitigate the SNR loss originating due to the latter reason. Since it is necessary to utilize static prior to regularization, the dynamic contrast-to-noise ratio (CNR) in parallel MRI will be affected. In this paper we investigate the CNR of regularized sensitivity encoding (SENSE) acquisitions. We propose to implement regularized parallel MRI acquisitions in functional MRI (fMRI) experiments by incorporating the prior from combined segmented echo-planar imaging (EPI) acquisition into SENSE reconstructions. We investigated the impact of regularization on the CNR by performing parametric simulations at various BOLD contrasts, acceleration rates, and sizes of the active brain areas. As quantified by receiver operating characteristic (ROC) analysis, the simulations suggest that the detection power of SENSE fMRI can be improved by regularized reconstructions, compared to unregularized reconstructions. Human motor and visual fMRI data acquired at different field strengths and array coils also demonstrate that regularized SENSE improves the detection of functionally active brain regions.

Evaluation on the generalization of a learned convolutional neural network for MRI reconstruction

Patient radiation dose is a major issue in computerized tomography (CT) imaging. Therefore, many improvements to the classical reconstruction algorithms are suggested to achieve reasonable image quality with less patient dose. The aim of this work is to improve the well-known algebraic reconstruction algorithm (ART) in order to obtain good image quality with less or limited projection angles. We achieve this purpose by sequential application of ART update, total variation minimization (TV), and non-local means (NLM). Both TV and NLM are widely used in imaging algorithms with high performance. To show the improvement in ART by TV and NLM we used a Shepp-Logan phantom simulation and real data from digital tomosynthesis imaging system. Our results indicate that the proposed method provided superior results over two widely used methods, ART and ART+TV, in many senses including Structure SIMilarity (SSIM), signal to noise ratio (SNR) and root mean squared error (RMSE).

We propose a rate-distortion optimization (RDO) scheme based on the structural similarity (SSIM) index, which was found to be a better indicator of perceived image quality than mean-squared error, but has not been fully exploited in the context of image and video coding. At the frame level, an adaptive Lagrange multiplier selection method is proposed based on a novel reduced-reference statistical SSIM estimation algorithm and a rate model that combines the side information with the entropy of the transformed residuals. At the macroblock level, the Lagrange multiplier is further adjusted based on an information theoretical approach that takes into account both the motion information content and perceptual uncertainty of visual speed perception. Finally, the mode for H.264/AVC coding is selected by the SSIM index and the adjusted Lagrange multiplier. Extensive experiments show that the proposed scheme can achieve significantly better rate-SSIM performance and provide better visual quality than conventional RDO coding schemes.