Dynamic MR image reconstruction based on total generalized variation and low-rank decomposition.
Ontology highlight
ABSTRACT: Purpose
Propose a novel decomposition-based model employing the total generalized variation (TGV) and the nuclear norm, which can be used in compressed sensing-based dynamic MR reconstructions.Theory and methods
We employ the nuclear norm to represent the time-coherent background and the spatiotemporal TGV functional for the sparse dynamic component above. We first design an algorithm using the classical first-order primal-dual method for solving the proposed model and then give the norm estimation for the convergence condition. The proposed model is compared with the state-of-the-art methods on different data sets under different sampling schemes and acceleration factors.Results
The proposed model achieves higher SERs and SSIMs than kt-SLR, kt-RPCA, L+S, and ICTGV on cardiac perfusion and breast DCE-MRI data sets under both the pseudoradial and the Cartesian sampling schemes. In addition, the proposed model better suppresses the spatial artifacts and preserves the edges.Conclusions
The proposed model outperforms the state-of-the-art methods and generates high-quality reconstructions under different sampling schemes and different acceleration factors.
SUBMITTER: Wang D
PROVIDER: S-EPMC7047634 | biostudies-literature |
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:Image super-resolution (SR) aims to recover high-resolution images from their low-resolution counterparts for improving image analysis and visualization. Interpolation methods, widely used for this purpose, often result in images with blurred edges and blocking effects. More advanced methods such as total variation (TV) retain edge sharpness during image recovery. However, these methods only utilize information from local neighborhoods, neglecting useful information from remote voxels. In this paper, we propose a novel image SR method that integrates both local and global information for effective image recovery. This is achieved by, in addition to TV, low-rank regularization that enables utilization of information throughout the image. The optimization problem can be solved effectively via alternating direction method of multipliers (ADMM). Experiments on MR images of both adult and pediatric subjects demonstrate that the proposed method enhances the details in the recovered high-resolution images, and outperforms methods such as the nearest-neighbor interpolation, cubic interpolation, iterative back projection (IBP), non-local means (NLM), and TV-based up-sampling.
| S-EPMC5572670 | biostudies-other
Project description:Total generalized variation (TGV)-based computed tomography (CT) image reconstruction, which utilizes high-order image derivatives, is superior to total variation-based methods in terms of the preservation of edge information and the suppression of unfavorable staircase effects. However, conventional TGV regularization employs l1-based form, which is not the most direct method for maximizing sparsity prior. In this study, we propose a total generalized p-variation (TGpV) regularization model to improve the sparsity exploitation of TGV and offer efficient solutions to few-view CT image reconstruction problems. To solve the nonconvex optimization problem of the TGpV minimization model, we then present an efficient iterative algorithm based on the alternating minimization of augmented Lagrangian function. All of the resulting subproblems decoupled by variable splitting admit explicit solutions by applying alternating minimization method and generalized p-shrinkage mapping. In addition, approximate solutions that can be easily performed and quickly calculated through fast Fourier transform are derived using the proximal point method to reduce the cost of inner subproblems. The accuracy and efficiency of the simulated and real data are qualitatively and quantitatively evaluated to validate the efficiency and feasibility of the proposed method. Overall, the proposed method exhibits reasonable performance and outperforms the original TGV-based method when applied to few-view problems.
| S-EPMC4764011 | biostudies-literature
Project description:In order to monitor dynamic physiological events in near-real time, a variety of photoacoustic computed tomography (PACT) systems have been developed that can rapidly acquire data. Previously reported studies of dynamic PACT have employed conventional static methods to reconstruct a temporally ordered sequence of images on a frame-by-frame basis. Frame-by-frame image reconstruction (FBFIR) methods fail to exploit correlations between data frames and are known to be statistically and computationally suboptimal. In this study, a low-rank matrix estimation-based spatiotemporal image reconstruction (LRME-STIR) method is investigated for dynamic PACT applications. The LRME-STIR method is based on the observation that, in many PACT applications, the number of frames is much greater than the rank of the ideal noiseless data matrix. Using both computer-simulated and experimentally measured photoacoustic data, the performance of the LRME-STIR method is compared with that of conventional FBFIR method followed by image-domain filtering. The results demonstrate that the LRME-STIR method is not only computationally more efficient but also produces more accurate dynamic PACT images than a conventional FBFIR method followed by image-domain filtering.
| S-EPMC4046831 | biostudies-other
Project description:PurposeThe proposed reconstruction framework addresses the reconstruction accuracy, noise propagation and computation time for magnetic resonance fingerprinting.MethodsBased on a singular value decomposition of the signal evolution, magnetic resonance fingerprinting is formulated as a low rank (LR) inverse problem in which one image is reconstructed for each singular value under consideration. This LR approximation of the signal evolution reduces the computational burden by reducing the number of Fourier transformations. Also, the LR approximation improves the conditioning of the problem, which is further improved by extending the LR inverse problem to an augmented Lagrangian that is solved by the alternating direction method of multipliers. The root mean square error and the noise propagation are analyzed in simulations. For verification, in vivo examples are provided.ResultsThe proposed LR alternating direction method of multipliers approach shows a reduced root mean square error compared to the original fingerprinting reconstruction, to a LR approximation alone and to an alternating direction method of multipliers approach without a LR approximation. Incorporating sensitivity encoding allows for further artifact reduction.ConclusionThe proposed reconstruction provides robust convergence, reduced computational burden and improved image quality compared to other magnetic resonance fingerprinting reconstruction approaches evaluated in this study. Magn Reson Med 79:83-96, 2018. © 2017 International Society for Magnetic Resonance in Medicine.
| S-EPMC5585028 | biostudies-literature
Project description:We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components either exactly or approximately. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information.
| S-EPMC5403160 | biostudies-literature
Project description:Purpose: Conventional iterative low-dose CBCT reconstruction techniques are slow and tend to over-smooth edges through uniform weighting of the image penalty gradient. In this study, we present a non-iterative analytical low-dose CBCT reconstruction technique by restoring the noisy low-dose CBCT projection with the non-local total variation (NLTV) method. Methods: We modeled the low-dose CBCT reconstruction as recovering high quality, high-dose CBCT x-ray projections (100 kVp, 1.6 mAs) from low-dose, noisy CBCT x-ray projections (100 kVp, 0.1 mAs). The restoration of CBCT projections was performed using the NLTV regularization method. In NLTV, the x-ray image is optimized by minimizing an energy function that penalizes gray-level difference between pair of pixels between noisy x-ray projection and denoising x-ray projection. After the noisy projection is restored by NLTV regularization, the standard FDK method was applied to generate the final reconstruction output. Results: Significant noise reduction was achieved comparing to original, noisy inputs while maintaining the image quality comparable to the high-dose CBCT projections. The experimental validations show the proposed NLTV algorithm can robustly restore the noise level of x-ray projection images while significantly improving the overall image quality. The improvement in normalized mean square error (NMSE) and peak signal-to-noise ratio (PSNR) measured from the non-local total variation-gradient projection (NLTV-GPSR) algorithm is noticeable compared to that of uncorrected low-dose CBCT images. Moreover, the difference of CNRs from the gains from the proposed algorithm is noticeable and comparable to high-dose CBCT. Conclusion: The proposed method successfully restores noise degraded, low-dose CBCT projections to high-dose projection quality. Such an outcome is a considerable improvement to the reconstruction result compared to the FDK-based method. In addition, a significant reduction in reconstruction time makes the proposed algorithm more attractive. This demonstrates the potential use of the proposed algorithm for clinical practice in radiotherapy.
| S-EPMC7056884 | biostudies-literature
Project description:PURPOSE:To accelerate dynamic MR applications using infimal convolution of total generalized variation functionals (ICTGV) as spatio-temporal regularization for image reconstruction. THEORY AND METHODS:ICTGV comprises a new image prior tailored to dynamic data that achieves regularization via optimal local balancing between spatial and temporal regularity. Here it is applied for the first time to the reconstruction of dynamic MRI data. CINE and perfusion scans were investigated to study the influence of time dependent morphology and temporal contrast changes. ICTGV regularized reconstruction from subsampled MR data is formulated as a convex optimization problem. Global solutions are obtained by employing a duality based non-smooth optimization algorithm. RESULTS:The reconstruction error remains on a low level with acceleration factors up to 16 for both CINE and dynamic contrast-enhanced MRI data. The GPU implementation of the algorithm suites clinical demands by reducing reconstruction times of one dataset to less than 4 min. CONCLUSION:ICTGV based dynamic magnetic resonance imaging reconstruction allows for vast undersampling and therefore enables for very high spatial and temporal resolutions, spatial coverage and reduced scan time. With the proposed distinction of model and regularization parameters it offers a new and robust method of flexible decomposition into components with different degrees of temporal regularity. Magn Reson Med 78:142-155, 2017. © 2016 International Society for Magnetic Resonance in Medicine.
| S-EPMC5553112 | biostudies-literature
Project description:The low-rank plus sparse (L+S) decomposition model enables the reconstruction of under-sampled dynamic parallel magnetic resonance imaging (MRI) data. Solving for the low-rank and the sparse components involves non-smooth composite convex optimization, and algorithms for this problem can be categorized into proximal gradient methods and variable splitting methods. This paper investigates new efficient algorithms for both schemes. While current proximal gradient techniques for the L+S model involve the classical iterative soft thresholding algorithm (ISTA), this paper considers two accelerated alternatives, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other with the recent proximal optimized gradient method (POGM). In the augmented Lagrangian (AL) framework, we propose an efficient variable splitting scheme based on the form of the data acquisition operator, leading to simpler computation than the conjugate gradient (CG) approach required by existing AL methods. Numerical results suggest faster convergence of the efficient implementations for both frameworks, with POGM providing the fastest convergence overall and the practical benefit of being free of algorithm tuning parameters.
| S-EPMC6867710 | biostudies-literature
Project description:To apply the low-rank plus sparse (L+S) matrix decomposition model to reconstruct undersampled dynamic MRI as a superposition of background and dynamic components in various problems of clinical interest.The L+S model is natural to represent dynamic MRI data. Incoherence between k-t space (acquisition) and the singular vectors of L and the sparse domain of S is required to reconstruct undersampled data. Incoherence between L and S is required for robust separation of background and dynamic components. Multicoil L+S reconstruction is formulated using a convex optimization approach, where the nuclear norm is used to enforce low rank in L and the l1 norm is used to enforce sparsity in S. Feasibility of the L+S reconstruction was tested in several dynamic MRI experiments with true acceleration, including cardiac perfusion, cardiac cine, time-resolved angiography, and abdominal and breast perfusion using Cartesian and radial sampling.The L+S model increased compressibility of dynamic MRI data and thus enabled high-acceleration factors. The inherent background separation improved background suppression performance compared to conventional data subtraction, which is sensitive to motion.The high acceleration and background separation enabled by L+S promises to enhance spatial and temporal resolution and to enable background suppression without the need of subtraction or modeling.
| S-EPMC4207853 | biostudies-literature
Project description:PURPOSE:Numerous image reconstruction methodologies for positron emission tomography (PET) have been developed that incorporate magnetic resonance (MR) imaging structural information, producing reconstructed images with improved suppression of noise and reduced partial volume effects. However, the influence of MR structural information also increases the possibility of suppression or bias of structures present only in the PET data (PET-unique regions). To address this, further developments for MR-informed methods have been proposed, for example, through inclusion of the current reconstructed PET image, alongside the MR image, in the iterative reconstruction process. In this present work, a number of kernel and maximum a posteriori (MAP) methodologies are compared, with the aim of identifying methods that enable a favorable trade-off between the suppression of noise and the retention of unique features present in the PET data. METHODS:The reconstruction methods investigated were: the MR-informed conventional and spatially compact kernel methods, referred to as KEM and KEM largest value sparsification (LVS) respectively; the MR-informed Bowsher and Gaussian MR-guided MAP methods; and the PET-MR-informed hybrid kernel and anato-functional MAP methods. The trade-off between improving the reconstruction of the whole brain region and the PET-unique regions was investigated for all methods in comparison with postsmoothed maximum likelihood expectation maximization (MLEM), evaluated in terms of structural similarity index (SSIM), normalized root mean square error (NRMSE), bias, and standard deviation. Both simulated BrainWeb (10 noise realizations) and real [18 F] fluorodeoxyglucose (FDG) three-dimensional datasets were used. The real [18 F]FDG dataset was augmented with simulated tumors to allow comparison of the reconstruction methodologies for the case of known regions of PET-MR discrepancy and evaluated at full counts (100%) and at a reduced (10%) count level. RESULTS:For the high-count simulated and real data studies, the anato-functional MAP method performed better than the other methods under investigation (MR-informed, PET-MR-informed and postsmoothed MLEM), in terms of achieving the best trade-off for the reconstruction of the whole brain and PET-unique regions, assessed in terms of the SSIM, NRMSE, and bias vs standard deviation. The inclusion of PET information in the anato-functional MAP method enables the reconstruction of PET-unique regions to attain similarly low levels of bias as unsmoothed MLEM, while moderately improving the whole brain image quality for low levels of regularization. However, for low count simulated datasets the anato-functional MAP method performs poorly, due to the inclusion of noisy PET information in the regularization term. For the low counts simulated dataset, KEM LVS and to a lesser extent, HKEM performed better than the other methods under investigation in terms of achieving the best trade-off for the reconstruction of the whole brain and PET-unique regions, assessed in terms of the SSIM, NRMSE, and bias vs standard deviation. CONCLUSION:For the reconstruction of noisy data, multiple MR-informed methods produce favorable whole brain vs PET-unique region trade-off in terms of the image quality metrics of SSIM and NRMSE, comfortably outperforming the whole image denoising of postsmoothed MLEM.
| S-EPMC6899618 | biostudies-literature