Improved dynamic MRI reconstruction by exploiting sparsity and rank-deficiency

In this paper we address the problem of dynamic MRI reconstruction from partially sampled K-space data. Our work is motivated by previous studies in this area that proposed exploiting the spatiotemporal correlation of the dynamic MRI sequence by posing the reconstruction problem as a least squares minimization regularized by sparsity and low-rank penalties. Ideally the sparsity and low-rank penalties should be represented by the l₀-norm and the rank of a matrix; however both are NP hard penalties. The previous studies used the convex l₁-norm as a surrogate for the l₀-norm and the non-convex Schatten-q norm (0 < q ≤ 1) as a surrogate for the rank of matrix. Following past research in sparse recovery, we know that non-convex l_p-norm (0 < p ≤ 1) is a better substitute for the NP hard l₀-norm than the convex l₁-norm. Motivated by these studies, we propose improvements over the previous studies by replacing the l₁-norm sparsity penalty by the l_p-norm. Thus, we reconstruct the dynamic MRI sequence by solving a least squares minimization problem regularized by l_p-norm as the sparsity penalty and Schatten-q norm as the low-rank penalty. There are no efficient algorithms to solve the said problems. In this paper, we derive efficient algorithms to solve them. The experiments have been carried out on Dynamic Contrast Enhanced (DCE) MRI datasets. Both quantitative and qualitative analysis indicates the superiority of our proposed improvement over the existing methods.     

Causal MRI reconstruction via Kalman prediction and compressed sensing correction

This technical note addresses the problem of causal online reconstruction of dynamic MRI, i.e. given the reconstructed frames till the previous time instant, we reconstruct the frame at the current instant. Our work follows a prediction-correction framework. Given the previous frames, the current frame is predicted based on a Kalman estimate. The difference between the estimate and the current frame is then corrected based on the k-space samples of the current frame; this reconstruction assumes that the difference is sparse. The method is compared against prior Kalman filtering based techniques and Compressed Sensing based techniques. Experimental results show that the proposed method is more accurate than these and considerably faster.     

Dynamic MRI reconstruction from highly undersampled (k,t)-space data using weighted Schatten p-norm regularizer of tensor

Combination of the low-rankness and sparsity has been successfully used to reconstruct desired dynamic magnetic resonance image (MRI) from highly-undersampled (k, t)-space data. However, nuclear norm, as a convex relaxation of the rank function, can cause the solution deviating from the original solution of low-rank problem. Moreover, equally treating different rank component is not flexible to deal with real applications. In this paper, an efficient reconstruction model is proposed to efficiently reconstruct dynamic MRI. First, we treat dynamic MRI as a 3rd-order tensor, and formulate the low-rankness via non-convex Schatten p-norm of matrices unfolded from the tensor. Secondly, we assign different weight for each rank component in Schatten p-norm. Furthermore, we combine the proposed weighted Schatten p-norm of a tensor as low-rank regularizer, and spatiotemporal total variation as sparse regularizer to formulate the reconstruction model for dynamic MRI. Thirdly, to efficiently solve the formulated reconstruction model, we derive an algorithm based on Bregman iterations with alternating direction multiplier. Over two public data sets of dynamic MRI, experiments demonstrate that the proposed method achieves much better quality.     

Causal dynamic MRI reconstruction via nuclear norm minimization

This work addresses the problem of online reconstruction of dynamic magnetic resonance images (MRI). The proposed method reconstructs the difference between the images of previous and current time frames. This difference image is modeled as a rank deficient matrix and is solved from the partially sampled k-space data via nuclear norm minimization. Our proposed method has been compared against state-of-the-art offline and online reconstruction methods. Our method has similar reconstruction accuracy as the offline method and significantly higher accuracy compared to the online technique. It is about an order of magnitude faster than the online technique compared against. Our experimental data consisted of dynamic MRI data that were collected at 6 to 7 frames per second and having resolutions of 128×128 and 256×256 pixels per frame. Experimental evaluation indicates that our proposed method is capable of reconstructing 128×128 images at the rate of 4 frames per second and 256×256 images at the rate of 2 frames per second. The previous online method requires about 3.75 s for reconstructing each image. The improvement in reconstruction speed is clearly discernible. Moreover, our method has a reconstruction error that is about half that of the previous online method.     

HCC-to-liver contrast on arterial-dominant phase images of EOB-enhanced MRI: comparison with dynamic CT

The purpose of this study was to assess the efficacy of arterial-dominant phase images of gadolinium–ethoxybenzyl–diethylenetriamine pentaacetic acid (EOB)-enhanced magnetic resonance imaging (MRI) for evaluation of arterial blood supply in hepatocellular carcinoma (HCC) in comparison with that of multiphasic dynamic computed tomography (CT). This study comprised 30 patients (22 men and 8 women, mean age: 68.0 years) with 40 pathologically proven HCCs (well differentiated: 3, moderately differentiated: 30, poorly differentiated: 7, mean diameter: 45.1 mm), all of whom underwent EOB-enhanced MRI and dynamic CT preoperative assessment. Regions of interest were placed over HCCs and the adjacent normal liver, and signal intensities or CT values were measured by two experienced abdominal radiologists on the arterial-dominant phase images of EOB-enhanced MRI and dynamic CT images. HCC-to-liver contrasts [Michelson's contrast: C_M=(S_HCC− S_Liver)/(S_HCC+ S_Liver)] were calculated and compared among the modalities. HCC-to-liver contrasts were also visually scored on a 5-point scale and compared. The mean C_M and visual score for dynamic CT were significantly higher than those for EOB-enhanced MRI. Good agreements were obtained among the two observers. Dynamic CT is a more suitable modality than EOB-enhanced MRI for evaluation of arterial blood supply in HCC. This should be taken into account for diagnosis and management of HCC.     

Sparsity-constrained SENSE reconstruction: An efficient implementation using a fast composite splitting algorithm

Parallel imaging and compressed sensing have been arguably the most successful and widely used techniques for fast magnetic resonance imaging (MRI). Recent studies have shown that the combination of these two techniques is useful for solving the inverse problem of recovering the image from highly under-sampled k-space data. In sparsity-enforced sensitivity encoding (SENSE) reconstruction, the optimization problem involves data fidelity (L2-norm) constraint and a number of L1-norm regularization terms (i.e. total variation or TV, and L1 norm). This makes the optimization problem difficult to solve due to the non-smooth nature of the regularization terms. In this paper, to effectively solve the sparsity-regularized SENSE reconstruction, we utilize a new optimization method, called fast composite splitting algorithm (FCSA), which was developed for compressed sensing MRI. By using a combination of variable splitting and operator splitting techniques, the FCSA algorithm decouples the large optimization problem into TV and L1 sub-problems, which are then, solved efficiently using existing fast methods. The operator splitting separates the smooth terms from the non-smooth terms, so that both terms are treated in an efficient manner. The final solution to the SENSE reconstruction is obtained by weighted solutions to the sub-problems through an iterative optimization procedure. The FCSA-based parallel MRI technique is tested on MR brain image reconstructions at various acceleration rates and with different sampling trajectories. The results indicate that, for sparsity-regularized SENSE reconstruction, the FCSA-based method is capable of achieving significant improvements in reconstruction accuracy when compared with the state-of-the-art reconstruction method.     

Exploiting rank deficiency and transform domain sparsity for MR image reconstruction

The reconstruction of magnetic resonance (MR) images from the partial samples of their k-space data using compressed sensing (CS)-based methods has generated a lot of interest in recent years. To reconstruct the MR images, these techniques exploit the sparsity of the image in a transform domain (wavelets, total variation, etc.). In a recent work, it has been shown that it is also possible to reconstruct MR images by exploiting their rank deficiency. In this work, it will be shown that, instead of exploiting the sparsity of the image or rank deficiency alone, better reconstruction results can be achieved by combining transform domain sparsity with rank deficiency.To reconstruct an MR image using its transform domain sparsity and its rank deficiency, this work proposes a combined l₁-norm (of the transform coefficients) and nuclear norm (of the MR image matrix) minimization problem. Since such an optimization problem has not been encountered before, this work proposes and derives a first-order algorithm to solve it.The reconstruction results show that the proposed approach yields significant improvements, in terms of both visual quality as well as the signal to noise ratio, over previous works that reconstruct MR images either by exploiting rank deficiency or by the standard CS-based technique popularly known as the ‘Sparse MRI.’     

Wavelet-based edge correlation incorporated iterative reconstruction for undersampled MRI

Undersampling k-space is an effective way to decrease acquisition time for MRI. However, aliasing artifacts introduced by undersampling may blur the edges of magnetic resonance images, which often contain important information for clinical diagnosis. Moreover, k-space data is often contaminated by the noise signals of unknown intensity. To better preserve the edge features while suppressing the aliasing artifacts and noises, we present a new wavelet-based algorithm for undersampled MRI reconstruction. The algorithm solves the image reconstruction as a standard optimization problem including a ?₂ data fidelity term and ?₁ sparsity regularization term. Rather than manually setting the regularization parameter for the ?₁ term, which is directly related to the threshold, an automatic estimated threshold adaptive to noise intensity is introduced in our proposed algorithm. In addition, a prior matrix based on edge correlation in wavelet domain is incorporated into the regularization term. Compared with nonlinear conjugate gradient descent algorithm, iterative shrinkage/thresholding algorithm, fast iterative soft-thresholding algorithm and the iterative thresholding algorithm using exponentially decreasing threshold, the proposed algorithm yields reconstructions with better edge recovery and noise suppression.     

Smoothly Clipped Absolute Deviation (SCAD) regularization for compressed sensing MRI Using an augmented Lagrangian scheme

PurposeCompressed sensing (CS) provides a promising framework for MR image reconstruction from highly undersampled data, thus reducing data acquisition time. In this context, sparsity-promoting regularization techniques exploit the prior knowledge that MR images are sparse or compressible in a given transform domain. In this work, a new regularization technique was introduced by iterative linearization of the non-convex smoothly clipped absolute deviation (SCAD) norm with the aim of reducing the sampling rate even lower than it is required by the conventional l₁ norm while approaching an l₀ norm.Materials and MethodsThe CS-MR image reconstruction was formulated as an equality-constrained optimization problem using a variable splitting technique and solved using an augmented Lagrangian (AL) method developed to accelerate the optimization of constrained problems. The performance of the resulting SCAD-based algorithm was evaluated for discrete gradients and wavelet sparsifying transforms and compared with its l₁-based counterpart using phantom and clinical studies. The k-spaces of the datasets were retrospectively undersampled using different sampling trajectories. In the AL framework, the CS-MRI problem was decomposed into two simpler sub-problems, wherein the linearization of the SCAD norm resulted in an adaptively weighted soft thresholding rule with a sparsity enhancing effect.ResultsIt was demonstrated that the proposed regularization technique adaptively assigns lower weights on the thresholding of gradient fields and wavelet coefficients, and as such, is more efficient in reducing aliasing artifacts arising from k-space undersampling, when compared to its l₁-based counterpart.ConclusionThe SCAD regularization improves the performance of l₁-based regularization technique, especially at reduced sampling rates, and thus might be a good candidate for some applications in CS-MRI.     

Motion predicted online dynamic MRI reconstruction from partially sampled k-space data

In this work we address the problem of reconstructing dynamic MRI sequences in an online fashion, i.e. reconstructing the current frame given that the previous frames have been already reconstructed. The reconstruction consists of a prediction and a correction step. The prediction step is based on an Auto-Regressive AR(1) model. Assuming that the prediction is good, the difference between the predicted frame and the actual frame (to be reconstructed) will be sparse. In the correction step, the difference between the predicted frame and the actual frame is estimated from partially sampled K-space data via a sparsity promoting least squares minimization problem. We have compared the proposed method with state-of-the-art methods in online dynamic MRI reconstruction. The experiments have been carried out on 2D and 3D Dynamic Contrast Enhanced (DCE) MRI datasets. Results show that our method yields the least reconstruction error.     

On optimal reconstruction of constitutive relations

In this investigation we develop and validate a computational method for reconstructing constitutive relations based on measurement data, applicable to problems arising in nonequilibrium thermodynamics and continuum mechanics. This parameter estimation problem is solved as PDE-constrained optimization using a gradient-based technique in the optimize-then-discretize framework. The principal challenge is that the control variable (i.e., the relation characterizing the constitutive property) is not a function of the independent variables in the problem, but of the state (dependent) variable. The proposed method allows one to reconstruct a smooth constitutive relation defined over a broad range of the dependent variable. It relies on three main ingredients: a computationally friendly expression for the cost functional gradient, Sobolev gradients used in lieu of discontinuous L₂ gradients, and a systematic technique for shifting the identifiability region. The performance of this approach is illustrated by the reconstruction of the temperature dependence of the thermal conductivity in a one-dimensional model problem.     

Optimization of hyperparameters for SMS reconstruction

PurposeSimultaneous multi-slice (SMS) imaging accelerates MRI data acquisition by exciting multiple image slices with a single radiofrequency pulse. Overlapping slices encoded in acquired signal are separated using a mathematical model, which requires estimation of image reconstruction kernels using calibration data. Several parameters used in SMS reconstruction impact the quality and fidelity of final images. Therefore, finding an optimal set of reconstruction parameters is critical to ensure that accelerated acquisition does not significantly degrade resulting image quality.MethodsGradient-echo echo planar imaging data were acquired with a range of SMS acceleration factors from a cohort of five volunteers with no known neurological pathology. Images were collected using two available phased-array head coils (a 48-channel array and a reduced diameter 32-channel array) that support SMS. Data from these coils were identically reconstructed offline using a range of coil compression factors and reconstruction kernel parameters. A hybrid space (k-x), externally-calibrated coil-by-coil slice unaliasing approach was used for image reconstruction. The image quality of the resulting reconstructed SMS images was assessed by evaluating correlations with identical echo-planar reference data acquired without SMS. A finger tapping functional MRI (fMRI) experiment was also performed and group analysis results were compared between data sets reconstructed with different coil compression levels.ResultsBetween the two RF coils tested in this study, the 32-channel coil with smaller dimensions clearly outperformed the larger 48-channel coil in our experiments. Generally, a large calibration region (144–192 samples) and small kernel sizes (2–4 samples) in k_y direction improved image quality. Use of regularization in the kernel fitting procedure had a notable impact on the fidelity of reconstructed images and a regularization value 0.0001 provided good image quality. With optimal selection of other hyperparameters in the hybrid space SMS unaliasing algorithm, coil compression caused small reduction in correlation between single-band and SMS unaliased images. Similarly, group analysis of fMRI results did not show a significant influence of coil compression on resulting image quality.ConclusionsThis study demonstrated that the hyperparameters used in SMS reconstruction need to be fine-tuned once the experimental factors such as the RF receive coil and SMS factor have been determined. A cursory evaluation of SMS reconstruction hyperparameter values is therefore recommended before conducting a full-scale quantitative study using SMS technologies.     

Dynamic cardiac MRI reconstruction using motion aligned locally low rank tensor (MALLRT)

Various sparse transform models have been explored for compressed sensing-based dynamic cardiac MRI reconstruction from vastly under-sampled k-space data. Recently emerged low rank tensor model using Tucker decomposition could be viewed as a special form of sparse model, where the core tensor, which is obtained using high-order singular value decomposition, is sparse in the sense that only a few elements have dominantly large magnitude. However, local details tend to be over-smoothed when the entire image is conventionally modeled as a global tensor. Moreover, low rankness is sensitive to motion as spatiotemporal correlation is corrupted by spatial misalignment between temporal frames. To overcome these limitations, this paper presents a novel motion aligned locally low rank tensor (MALLRT) model for dynamic MRI reconstruction. In MALLRT, low rank constraint is enforced on image patch-based local tensors, which correspond to overlapping blocks extracted from the reconstructed high-dimensional image after group-wise inter-frame motion registration. For solving the proposed model, this paper presents an efficient optimization algorithm by using variable splitting and alternating direction method of multipliers (ADMM). MALLRT demonstrated promising performance as validated on one cardiac perfusion MRI dataset and two cardiac cine MRI datasets using retrospective under-sampling with various acceleration factors, as well as one prospectively under-sampled cardiac perfusion MRI dataset. Compared to four state-of-the-art methods, MALLRT achieved substantially better image reconstruction quality in terms of both signal to error ratio (SER) and structural similarity index (SSIM) metrics, and visual perception in preserving spatial details and capturing temporal variations.     

Composite pulses for RF phase encoded MRI: A simulation study

BackgroundIn B₁ encoded MRI, a realistic non-linear phase RF encoding coil will generate an inhomogeneous B₁ field that leads to spatially dependent flip angles. The non-linearity of the B₁ phase gradient can be compensated for in the reconstruction, but B₁ inhomogeneity remains a problem. The effect of B₁ inhomogeneity on tip angles for conventional, B₀ encoded MRI, may be minimized using composite pulses. The objective of this study was to explore the feasibility of using composite pulses with non-linear RF phase encoding coils and to identify the most appropriate composite pulse scheme.MethodsRF encoded signals were simulated via the Bloch equation for various symmetric, asymmetric and antisymmetric composite pulses. The simulated signals were reconstructed using a constrained least squares method.ResultsRoot mean square reconstruction errors varied from 6% (for an asymmetric composite pulse) to 9.7% (for an antisymmetric composite pulse).ConclusionAn asymmetric composite pulse scheme created images with fewer artifacts than other composite pulse schemes in inhomogeneous B₀ and B₁ fields making it the best choice for decreasing the effects of spatially varying flip angles. This is contrary to the conclusion that antisymmetric composite pulses are the best ones to use for spin echo sequences in conventional, B₀ encoded, MRI.     

Evaluation of solitary pulmonary nodules with dynamic contrast-enhanced MR imaging—a promising technique?

The evaluation of a solitary pulmonary nodule (SPN) is one of the most frequently encountered challenges in thoracic radiology. In addition to a “state-of-the-art” evaluation of SPNs with CT and biopsy techniques, recently the assessment of the enhancement characteristics with iodinized contrast agents has shown its potential to improve the characterization of SPNs. We investigated whether dynamic contrast-enhanced MRI is suitable to assess the degree and kinetics of MR contrast enhancement and whether this technique could help in the noninvasive specification of SPNs. We studied prospectively 21 patients with SPNs. T₁-weighted and proton density-weighted spoiled gradient-echo breath-hold images (2D-FLASH) were obtained before and after the administration of Gd-DTPA in a standard dosage of 0.1 mmol/kg body weight. The maximum enhancement and the initial velocity of contrast uptake were assessed and correlated with pathohistological findings. To quantify contrast enhancement, we used the relative signal intensity increase (S_rel) and the recently introduced enhancement factor (EF) and contrast uptake equivalent (CE). Dynamic contrast-enhanced MRI proved to be well suited for the assessment of the contrast enhancement characteristics of SPNs. Significant differences were found in the degree and kinetics of contrast enhancement for specific types of nodules. Malignant neoplastic SPNs enhanced stronger and faster than benign neoplastic SPNs. The strongest and fastest enhancement, however, was found in a benign type of nodules where histology revealed inflammatory/fibrous lesions. These differences in contrast enhancement between the different pathohistological groups were more significant when EF and CE rather than S_rel was used for the quantification of contrast enhancement. The results of this study indicate a potential role for dynamic contrast-enhanced MRI in the preoperative noninvasive evaluation of SPNs using EF and CE as contrast uptake assessment parameters.     

Real-time imaging with radial GRAPPA: Implementation on a heterogeneous architecture for low-latency reconstructions

Combination of non-Cartesian trajectories with parallel MRI permits to attain unmatched acceleration rates when compared to traditional Cartesian MRI during real-time imaging. However, computationally demanding reconstructions of such imaging techniques, such as k-space domain radial generalized auto-calibrating partially parallel acquisitions (radial GRAPPA) and image domain conjugate gradient sensitivity encoding (CG-SENSE), lead to longer reconstruction times and unacceptable latency for online real-time MRI on conventional computational hardware. Though CG-SENSE has been shown to work with low-latency using a general purpose graphics processing unit (GPU), to the best of our knowledge, no such effort has been made for radial GRAPPA. Radial GRAPPA reconstruction, which is robust even with highly undersampled acquisitions, is not iterative, requiring only significant computation during initial calibration while achieving good image quality for low-latency imaging applications. In this work, we present a very fast, low-latency, reconstruction framework based on a heterogeneous system using multi-core CPUs and GPUs. We demonstrate an implementation of radial GRAPPA that permits reconstruction times on par with or faster than acquisition of highly accelerated datasets in both cardiac and dynamic musculoskeletal imaging scenarios. Acquisition and reconstruction times are reported.     

Visually weighted reconstruction of compressive sensing MRI

Compressive sensing (CS) enables the reconstruction of a magnetic resonance (MR) image from undersampled data in k-space with relatively low-quality distortion when compared to the original image. In addition, CS allows the scan time to be significantly reduced. Along with a reduction in the computational overhead, we investigate an effective way to improve visual quality through the use of a weighted optimization algorithm for reconstruction after variable density random undersampling in the phase encoding direction over k-space. In contrast to conventional magnetic resonance imaging (MRI) reconstruction methods, the visual weight, in particular, the region of interest (ROI), is investigated here for quality improvement. In addition, we employ a wavelet transform to analyze the reconstructed image in the space domain and fully utilize data sparsity over the spatial and frequency domains. The visual weight is constructed by reflecting the perceptual characteristics of the human visual system (HVS), and then applied to ?₁ norm minimization, which gives priority to each coefficient during the reconstruction process. Using objective quality assessment metrics, it was found that an image reconstructed using the visual weight has higher local and global quality than those processed by conventional methods.     

High-performance rapid MR parameter mapping using model-based deep adversarial learning

PurposeTo develop and evaluate a deep adversarial learning-based image reconstruction approach for rapid and efficient MR parameter mapping.MethodsThe proposed method provides an image reconstruction framework by combining the end-to-end convolutional neural network (CNN) mapping, adversarial learning, and MR physical models. The CNN performs direct image-to-parameter mapping by transforming a series of undersampled images directly into MR parameter maps. Adversarial learning is used to improve image sharpness and enable better texture restoration during the image-to-parameter conversion. An additional pathway concerning the MR signal model is added between the estimated parameter maps and undersampled k-space data to ensure the data consistency during network training. The proposed framework was evaluated on T₂ mapping of the brain and the knee at an acceleration rate R = 8 and was compared with other state-of-the-art reconstruction methods. Global and regional quantitative assessments were performed to demonstrate the reconstruction performance of the proposed method.ResultsThe proposed adversarial learning approach achieved accurate T₂ mapping up to R = 8 in brain and knee joint image datasets. Compared to conventional reconstruction approaches that exploit image sparsity and low-rankness, the proposed method yielded lower errors and higher similarity to the reference and better image sharpness in the T₂ estimation. The quantitative metrics were normalized root mean square error of 3.6% for brain and 7.3% for knee, structural similarity index of 85.1% for brain and 83.2% for knee, and tenengrad measures of 9.2% for brain and 10.1% for the knee. The adversarial approach also achieved better performance for maintaining greater image texture and sharpness in comparison to the CNN approach without adversarial learning.ConclusionThe proposed framework by incorporating the efficient end-to-end CNN mapping, adversarial learning, and physical model enforced data consistency is a promising approach for rapid and efficient reconstruction of quantitative MR parameters.     

Research and progress in magnetic resonance imaging of triple-negative breast cancer

Triple-negative breast cancer (TNBC), which characterized by distinct biological and clinical pathological features, has a worse prognosis because the lack of effective therapeutic targets. Breast MR is the most accurate imaging modality for diagnosis of breast cancer currently. MR imaging recognition could assist in diagnosis, pretreatment planning and prognosis evaluation of TNBC. MR findings of a larger solitary lesion, mass with smooth mass margin, high signal intensity on T₂-weighted images and rim enhancement are typical MRI features associated with TNBC. Further work is necessary about the clinical application of dynamic contrast-enhanced MR imaging (DCE-MRI), DWI and MRS.     

Non-Iterative Regularized reconstruction Algorithm for Non-CartesiAn MRI: NIRVANA

We introduce a novel noniterative algorithm for the fast and accurate reconstruction of nonuniformly sampled MRI data. The proposed scheme derives the reconstructed image as the nonuniform inverse Fourier transform of a compensated dataset. We derive each sample in the compensated dataset as a weighted linear combination of a few measured k-space samples. The specific k-space samples and the weights involved in the linear combination are derived such that the reconstruction error is minimized. The computational complexity of the proposed scheme is comparable to that of gridding. At the same time, it provides significantly improved accuracy and is considerably more robust to noise and undersampling. The advantages of the proposed scheme makes it ideally suited for the fast reconstruction of large multidimensional datasets, which routinely arise in applications such as f-MRI and MR spectroscopy. The comparisons with state-of-the-art algorithms on numerical phantoms and MRI data clearly demonstrate the performance improvement.