Dynamic Magnetic Resonance Imaging Data Research Articles

Compressed SVD-based L + S model to reconstruct undersampled dynamic MRI data using parallel architecture.

Magnetic Resonance Imaging (MRI) is a highly demanded medical imaging system due to high resolution, large volumetric coverage, and ability to capture the dynamic and functional information of body organs e.g. cardiac MRI is employed to assess cardiac structure and evaluate blood flow dynamics through the cardiac valves. Long scan time is the main drawback of MRI, which makes it difficult for the patients to remain still during the scanning process. By collecting fewer measurements, MRI scan time can be shortened, but this undersampling causes aliasing artifacts in the reconstructed images. Advanced image reconstruction algorithms have been used in literature to overcome these undersampling artifacts. These algorithms are computationally expensive and require a long time for reconstruction which makes them infeasible for real-time clinical applications e.g. cardiac MRI. However, exploiting the inherent parallelism in these algorithms can help to reduce their computation time. Low-rank plus sparse (L+S) matrix decomposition model is a technique used in literature to reconstruct the highly undersampled dynamic MRI (dMRI) data at the expense of long reconstruction time. In this paper, Compressed Singular Value Decomposition (cSVD) model is used in L+S decomposition model (instead of conventional SVD) to reduce the reconstruction time. The results provide improved quality of the reconstructed images. Furthermore, it has been observed that cSVD and other parts of the L+S model possess highly parallel operations; therefore, a customized GPU based parallel architecture of the modified L+S model has been presented to further reduce the reconstruction time. Four cardiac MRI datasets (three different cardiac perfusion acquired from different patients and one cardiac cine data), each with different acceleration factors of 2, 6 and 8 are used for experiments in this paper. Experimental results demonstrate that using the proposed parallel architecture for the reconstruction of cardiac perfusion data provides a speed-up factor up to 19.15× (with memory latency) and 70.55× (without memory latency) in comparison to the conventional CPU reconstruction with no compromise on image quality. The proposed method is well-suited for real-time clinical applications, offering a substantial reduction in reconstruction time.

Low-rank plus sparse joint smoothing model based on tensor singular value decomposition for dynamic MRI reconstruction

Dynamic magnetic resonance imaging (DMRI) is an important medical imaging modality, but the long imaging time limits its practical applications. This paper proposes a low-rank plus sparse joint smoothing model based on tensor singular value decomposition (T-SVD) to reconstruct DMR images from highly under-sampled k-t space data. The low-rank plus sparse tensor (ℒ+S) model decomposes the DMR data into a low-rank and sparse tensor, which naturally fits the dynamic MR images characteristics and exploits the spatiotemporal correlation of DMRI data to improve reconstruction effect. T-SVD is utilized in the ℒ+S model to maintain the intrinsic structure of the low-rank tensor and further enhance the low-rank property. In addition, considering the global multi-dimensional smoothness of the DMR images, the proposed method joint tensor total variation (TTV) constraints to utilize the smoothness of DMR images to obtain more reconstruction details while protecting the global structure. We conducted experiments on the dynamic cardiac datasets, and the experiment results show that the proposed method has superior performance to several state-of-the-art imaging methods.

Tiroid Karsinomu Tanısı – Problem Çözücü Olarak Dinamik Manyetik Rezonans Görüntüleme

Objective: Comparison of the diagnostic accuracy of dynamic magnetic resonance imaging (MRI) with color Doppler US and Fine Needle Aspiration Cytology (FNAC) in the differential diagnosis of thyroid carcinoma cases.
 Materials and methods: Study group comprised 28 women and 6 men and all of them had thyroid hormone disorders in their routine examinations. 38 nodules were examined. After radiologic examinations, FNAC and thyroidectomy were applied.
 Results: The dynamic MR was found to have the highest sensitivity and specificity between the color-Doppler US, FNAC, and dynamic MR modalities for the diagnosis of carcinoma. In the dynamic MR examination, the difference between the peak-contrast signal intensity values (p = 0.018) and the minimum-contrast signal intensity values (p = 0.023) calculated at the p < 0.05 level were statistically significant between the malignant and benign nodules.
 Conclusions: We consider that the differential diagnosis of thyroid nodules can be made by analyzing the dynamic MRI data. Malignant thyroid nodules show typical time-signal intensity curves, and we believe that dynamic MRI will be valuable for preoperative assessment of the thyroid nodules in certain conditions like radiology–pathology mismatch.

Parallel non-Cartesian spatial-temporal dictionary learning neural networks (stDLNN) for accelerating 4D-MRI.

Dynamic magnetic resonance imaging (MRI) acquisitions are relatively slow due to physical and physiological limitations. The spatial-temporal dictionary learning (DL) approach accelerates dynamic MRI by learning spatial-temporal correlations, but the regularization parameters need to be manually adjusted, the performance at high acceleration rate is limited, and the reconstruction can be time-consuming. Deep learning techniques have shown good performance in accelerating MRI due to the powerful representational capabilities of neural networks. In this work, we propose a parallel non-Cartesian spatial-temporal dictionary learning neural networks (stDLNN) framework that combines dictionary learning with deep learning algorithms and utilizes the spatial-temporal prior information of dynamic MRI data to achieve better reconstruction quality and efficiency. The coefficient estimation modules (CEM) are designed in the framework to adaptively adjust the regularization coefficients. Experimental results show that combining dictionary learning with deep neural networks and using spatial-temporal dictionaries can obviously improve the image quality and computational efficiency compared with the state-of-the-art non-Cartesian imaging methods for accelerating the 4D-MRI especially at high acceleration rate.

Time-Synchronized MRI-Assessment of Respiratory Apparatus Subsystems—A Feasibility Study

The thorax (TH), the thoracic diaphragm (TD), and the abdominal wall (AW) are three sub-systems of the respiratory apparatus whose displacement motion has been well studied with the use of magnetic resonance imaging (MRI). Another sub-system, which has however received less research attention with respect to breathing, is the pelvic floor (PF). In particular, there is no study that has investigated the displacement of all four sub-systems simultaneously. Addressing this issue, it was the purpose of this feasibility study to establish a data acquisition paradigm for time-synchronous quantitative analysis of dynamic MRI data from these four major contributors to respiration and phonation (TH, TD, AW, and PF). Three healthy females were asked to breathe in and out forcefully while being recorded in a 1.5-Tesla whole body MR-scanner. Spanning a sequence of 15.12 seconds, 40 MRI data frames were acquired. Each data frame contained two slices, simultaneously documenting the mid-sagittal (TH, TD, PF) and transversal (AW) planes. The displacement motion of the four anatomical structures of interest was documented using kymographic analysis, resulting in time-varying calibrated structure displacement data. After computing the fundamental frequency of the cyclical breathing motion, the phase offsets of the TH, PF, and AW with respect to the TD were computed. Data analysis revealed three fundamentally different displacement patterns. Total structure displacement was in the range of 0.94 cm (TH) to 4.27cm (TD). Phase delays of up to 90∘ (i.e., a quarter of a breathing cycle) between different structures were found. Motion offsets in the range of -28.30∘ to 14.90∘ were computed for the PF with respect to the TD. The diversity of results in only three investigated participants suggests a variety of possible breathing strategies, warranting further research.

Quantitative classification of invasive and noninvasive breast cancer using dynamic magnetic resonance imaging of the mammary gland.

ObjectivesBreast cancers are classified as invasive or noninvasive based on histopathological findings. Although time-intensity curve (TIC) analysis using magnetic resonance imaging (MRI) can differentiate benign from malignant disease, its diagnostic ability to quantitatively distinguish between invasive and noninvasive breast cancers has not been determined. In this study, we evaluated the ability of TIC analysis of dynamic MRI data (MRI-TIC) to distinguish between invasive and noninvasive breast cancers.Material and MethodsWe collected and analyzed data for 429 cases of epithelial invasive and noninvasive breast carcinomas. TIC features were extracted in washout areas suggestive of malignancy.ResultsThe graph determining the positive diagnosis rate for invasive and noninvasive cases revealed that the cut-off θi/ni value was 21.6° (invasive: θw > 21.6°, noninvasive: θw ≤ 21.6°). Tissues were classified as invasive or noninvasive using this cut-off value, and each result was compared with the histopathological diagnosis. Using this method, the accuracy of tissue classification by MRI-TIC was 88.6% (380/429), which was higher than that using ultrasound (73.4%, 315/429).ConclusionMRI-TIC is effective for the classification of invasive vs. noninvasive breast cancer.

Characterization of surface motion patterns in highly deformable soft tissue organs from dynamic MRI: An application to assess 4D bladder motion

Background and objectives: Dynamic Magnetic Resonance Imaging (MRI) may capture temporal anatomical changes in soft tissue organs with high-contrast but the obtained sequences usually suffer from limited volume coverage which makes the high-resolution reconstruction of organ shape trajectories a major challenge in temporal studies. Because of the variability of abdominal organ shapes across time and subjects, the objective of the present study is to go towards 3D dense velocity measurements to fully cover the entire surface and to extract meaningful features characterizing the observed organ deformations and enabling clinical action or decision.Methods: We present a pipeline for characterization of bladder surface dynamics during deep respiratory movements. For a compact shape representation, the reconstructed temporal volumes were first used to establish subject-specific dynamical 4D mesh sequences using the large deformation diffeomorphic metric mapping (LDDMM) framework. Then, we performed a statistical characterization of organ dynamics from mechanical parameters such as mesh elongations and distortions. Since we refer to organs as non-flat surfaces, we have also used the mean curvature change as metric to quantify surface evolution. However, the numerical computation of curvature is strongly dependant on the surface parameterization (i.e. the mesh resolution). To cope with this dependency, we employed a non-parametric method for surface deformation analysis. Independent of parameterization and minimizing the length of the geodesic curves, it stretches smoothly the surface curves towards a sphere by minimizing a Dirichlet energy. An Eulerian PDE approach is used to derive a shape descriptor from the curve-shortening flow. Intercorrelations between individuals’ motion patterns are computed using the Laplace-Beltrami Operator (LBO) eigenfunctions for spherical mapping.Results: Application to extracting characterization correlation curves for locally-controlled simulated shape trajectories demonstrates the stability of the proposed shape descriptor. Its usability was shown on MRI acquired for seven healthy participants for which the bladder was highly deformed by maximum of inspiration. As expected, the study showed that deformations occured essentially on the top lateral regions.Conclusion:Promising results were obtained, showing the organ in its 3D complexity during deformation due to strain conditions. Smooth genus-0 manifold reconstruction from sparse dynamic MRI data is employed to perform a statistical shape analysis for the determination of bladder deformation.

A Magnetic Resonance Imaging-Compatible Device to Perform In Vivo Anterior Knee Joint Loading.

Greater anterior knee laxity (AKL) is associated with impaired sensory input and decreased functional knee stability. As functional magnetic resonance imaging (MRI) is the gold standard for understanding brain function, methods to load the anterior cruciate ligament in the MRI environment could further our understanding of the ligament's sensory role in knee joint stability. To design and validate an MRI-compatible anterior knee joint loading device. Descriptive laboratory study. University laboratory study. Sixteen healthy and physically active females participated (age = 23.4 [3.7]y; mass = 64.4 [8.4]kg). The AKL was assessed by a commercially available arthrometer. The AKL was also assessed with a custom-made, MRI-compatible device that produced anterior knee joint loading in a manner similar to the commercial arthrometer while obtaining dynamic structural MRI data. The AKL (in millimeters) at 133N of loading was assessed with the commercial knee arthrometer. Anterior displacement of the tibia relative to the femur obtained at 133N of loading was measured from dynamic MRI data obtained during usage of the custom device. Pearson correlations were used to examine relationships between the 2 measures. The 95% limits of agreement compared the absolute differences between the 2 devices. There was a 3.2-mm systematic difference between AKL (6.3 [1.6]mm) and anterior tibial translation (3.2 [1.0]mm) measures. There was a significant positive correlation between values obtained from the commercial arthrometer and the MRI-compatible device values (r = .553, P = .026). While systematic differences were observed, the MRI-compatible anterior knee joint loading device anteriorly translated the tibia relative to the femur in a similar manner to a commercial arthrometer design to stress the anterior cruciate ligament. Such a device may be beneficial in future functional magnetic resonance imaging study of anterior cruciate ligament mechanoreception.

Dynamic sleep MRI in obstructive sleep apnea: a systematic review and meta-analysis.

PurposeThe objective of this study is to systematically review the international literature for dynamic sleep magnetic resonance imaging (MRI) as a diagnostic tool in obstructive sleep apnea (OSA), to perform meta-analysis on the quantitative data from the review, and to discuss its implications in future research and potential clinical applications.Study designA comprehensive review of the literature was performed, followed by a detailed analysis of the relevant data that has been published on the topic.MethodsClinical key, Uptodate, Ovid, Ebscohost, Pubmed/MEDLINE, Scopus, Dynamed, Web of Science and The Cochrane Library were systematically searched. Once the search was completed, dynamic sleep MRI data were analyzed.ResultsNineteen articles reported on 410 OSA patients and 79 controls that underwent dynamic sleep MRI and were included in this review. For meta-analysis of dynamic sleep MRI data, eight articles presented relevant data on 160 OSA patients. Obstruction was reported as follows: retropalatal (RP) 98%, retroglossal (RG) 41% and hypopharyngeal (HP) in 5%. Lateral pharyngeal wall (LPW) collapse was found in 35/73 (48%) patients. The combinations of RP + RG were observed in 24% and RP + RG + LPW in 16%. If sedation was used, 98% of study participants fell asleep compared to 66% of unsedated participants.ConclusionsDynamic sleep MRI has demonstrated that nearly all patients have retropalatal obstruction, retroglossal obstruction is common and hypopharyngeal obstruction is rare. Nearly all patients (98%) who are sedated are able to fall asleep during the MRI. There is significant heterogeneity in the literature and standardization is needed.Supplementary InformationThe online version contains supplementary material available at 10.1007/s00405-021-06942-y.

Evaluation of dynamic MRI data in patients with herniated intervertebral discs after the complex treatment including osteopathic correction

Introduction. Pain in the lumbosacral region is one of the most common causes of disability and medical attention acquiring. Magnetic resonance imaging (MRI) of the spine in these patients quite often demonstrates multiple hernias. Despite the success of modern, including complex, methods of treating patients with herniated discs of lumbosacral spine, the problem of objective revealing of the applied therapy effect with modern instrumental examination methods is actual.The goal of research — study was to study the changes in the MRI picture in patients with herniated intervertebral discs during treatment with inclusion of osteopathic correction.Materials and methods. The study involved 15 patients with herniated intervertebral discs of lumbosacral spine. The patients received outpatient conservative treatment with inclusion of osteopathic correction. Participants underwent MRI of the lumbar spine at the beginning of the study and 3 months after treatment. The obtained data were processed by methods of nonparametric statistics.Results. After the complex treatment, such indicators of MRI as the hernia size, the lateral pocket width and the pelvis configuration significantly improved. These parameters are important indicators of pathomorphological changes in the spinal motion segment, affecting the discoradicular conflict. At the same time, there were no obtained convincing data about the therapy effect on the L5 vertebra rotation, on the presence of sequestration and changes in the Tchaikovsky index. Perhaps this is due to the small sample and short follow-up period for patients.Conclusion. After the course of treatment with inclusion of osteopathic correction, the statistically significant changes in MRI images were revealed in patients with herniated intervertebral discs, indicating a positive dynamics in the parameters of the hernia size, the width of the lateral pocket and the configuration of the pelvis.

Smooth robust tensor principal component analysis for compressed sensing of dynamic MRI

Dynamic magnetic resonance imaging (DMRI) often requires a long time for measurement acquisition, and it is a crucial problem about the enhancement of reconstruction quality from a limited set of under-samples. The low-rank plus sparse decomposition model, which is also called robust principal component analysis (RPCA), is widely used for reconstruction of DMRI data in the model-based way. In this paper, considering that DMRI data are naturally in tensor form with block-wise smoothness, we propose a smooth robust tensor principal component analysis (SRTPCA) method for DMRI reconstruction. Compared with classical RPCA approaches, the low rank and sparsity terms are extended to tensor versions to fully exploit the spatial and temporal data structures. Moreover, a tensor total variation regularization term is used to encourage the multi-dimensional block-wise smoothness for the reconstructed DMRI data. The relaxed convex optimization model can be divided into several sub-problems by the alternating direction method of multipliers. Numerical experiments on cardiac perfusion and cine datasets demonstrate that the proposed SRTPCA method outperforms the state-of-the-art ones in terms of recovery accuracy.

Manifold Constrained Low-Rank and Joint Sparse Learning for Dynamic Cardiac MRI

Reconstruction from highly accelerated dynamic magnetic resonance imaging (MRI) is of great significance for medical diagnosis. The application of low-rank and sparse matrix decomposition to MRI can improve imaging speed and efficiency. However, the consistence of the learned low-rank and sparse structures for similar input samples is not well addressed in literature. In this paper, we propose a manifold constrained low-rank and joint sparse learning model that embeds the manifold priors into low-rank and joint sparse decomposition. It is noted that the joint sparsity is investigated to exploit the shared information. Further, the manifold constraints for low-rank and joint sparse parts are forced the optimization process to satisfy the structure preservation requirement. To solve the above manifold learning problem, a manifold constrained alternating direction method of multipliers ( McADMM ) approach is designed. It is proved theoretically that the sequence generated by McADMM converges to a stationary point. Numerical comparisons on simulation data and real-world dynamic cardiac MRI data are presented to demonstrate its efficiency.

A Kalman-Based Approach With EM Optimization for Respiratory Motion Modeling in Medical Imaging

Respiratory motion degrades quantitative and qualitative analysis of medical images. Estimation and, hence, correction of motion commonly uses static correspondence models between an external surrogate signal and internal motion. This paper presents a patient specific respiratory motion model with the ability to adapt in the presence of irregular motion via a Kalman filter with expectation maximization for parameter estimation. The adaptive approach introduces generalizability allowing the model to account for a broader variety of motion. This may be required in the presence of irregular breathing and with different sensors monitoring the external surrogate signal. The motion model framework utilizing an adaptive Kalman filter approach is tested on dynamic magnetic resonance imaging data of nine volunteers and compared to a state-of-the-art static total least squares approach. Results demonstrate the framework is capable of reducing motion to the order of ${p} ) more effective in the presence of irregular motion, assessed using the ${F}$ -test for model comparison. Utilizing the total sum of squares of estimated vector field error from the calculated ground truth, we observe approximately a fifty percent reduction in root mean square error and thirty percent reduction in standard deviation utilizing the Kalman model (EKF) in comparison to a static counterpart.

Orthogonal tensor dictionary learning for accelerated dynamic MRI.

A direct application of the compressed sensing (CS) theory to dynamic magnetic resonance imaging (MRI) reconstruction needs vectorization or matricization of the dynamic MRI data, which is composed of a stack of 2D images and can be naturally regarded as a tensor. This 1D/2D model may destroy the inherent spatial structure property of the data. An alternative way to exploit the multidimensional structure in dynamic MRI is to employ tensor decomposition for dictionary learning, that is, learning multiple dictionaries along each dimension (mode) and sparsely representing the multidimensional data with respect to the Kronecker product of these dictionaries. In this work, we introduce a novel tensor dictionary learning method under an orthonormal constraint on the elementary matrix of the tensor dictionary for dynamic MRI reconstruction. The proposed algorithm alternates sparse coding, tensor dictionary learning, and updating reconstruction, and each corresponding subproblem is efficiently solved by a closed-form solution. Numerical experiments on phantom and synthetic data show significant improvements in reconstruction accuracy and computational efficiency obtained by the proposed scheme over the existing method that uses the 1D/2D model with overcomplete dictionary learning. Graphical abstract Fig. 1 Comparison between (a) the traditional method and (b) the proposed method based on dictionary learning for dynamic MRI reconstruction.

Quantification of liver function by linearization of a two-compartment model of gadoxetic acid uptake using dynamic contrast-enhanced magnetic resonance imaging.

Dynamic gadoxetic acid-enhanced magnetic resonance imaging (MRI) allows the investigation of liver function through the observation of the perfusion and uptake of contrast agent in the parenchyma. Voxel-by-voxel quantification of the contrast uptake rate (k1 ) from dynamic gadoxetic acid-enhanced MRI through the standard dual-input, two-compartment model could be susceptible to overfitting of variance in the data. The aim of this study was to develop a linearized, but more robust, model. To evaluate the estimated k1 values using this linearized analysis, high-temporal-resolution gadoxetic acid-enhanced MRI scans were obtained in 13 examinations, and k1 maps were created using both models. Comparison of liver k1 values estimated from the two methods produced a median correlation coefficient of 0.91 across the 12 scans that could be used. Temporally sparse clinical MRI data with gadoxetic acid uptake were also employed to create k1 maps of 27 examinations using the linearized model. Of 20 scans, the created k1 maps were compared with overall liver function as measured by indocyanine green (ICG) retention, and yielded a correlation coefficient of 0.72. In the 27k1 maps created via the linearized model, the mean liver k1 value was 3.93±1.79mL/100mL/min, consistent with previous studies. The results indicate that the linearized model provides a simple and robust method for the assessment of the rate of contrast uptake that can be applied to both high-temporal-resolution dynamic contrast-enhanced MRI and typical clinical multiphase MRI data, and that correlates well with the results of both two-compartment analysis and independent whole liver function measurements.

Improving temporal resolution in fMRI using a 3D spiral acquisition and low rank plus sparse (L+S) reconstruction

Rapid whole-brain dynamic Magnetic Resonance Imaging (MRI) is of particular interest in Blood Oxygen Level Dependent (BOLD) functional MRI (fMRI). Faster acquisitions with higher temporal sampling of the BOLD time-course provide several advantages including increased sensitivity in detecting functional activation, the possibility of filtering out physiological noise for improving temporal SNR, and freezing out head motion. Generally, faster acquisitions require undersampling of the data which results in aliasing artifacts in the object domain. A recently developed low-rank (L) plus sparse (S) matrix decomposition model (L+S) is one of the methods that has been introduced to reconstruct images from undersampled dynamic MRI data. The L+S approach assumes that the dynamic MRI data, represented as a space-time matrix M, is a linear superposition of L and S components, where L represents highly spatially and temporally correlated elements, such as the image background, while S captures dynamic information that is sparse in an appropriate transform domain. This suggests that L+S might be suited for undersampled task or slow event-related fMRI acquisitions because the periodic nature of the BOLD signal is sparse in the temporal Fourier transform domain and slowly varying low-rank brain background signals, such as physiological noise and drift, will be predominantly low-rank. In this work, as a proof of concept, we exploit the L+S method for accelerating block-design fMRI using a 3D stack of spirals (SoS) acquisition where undersampling is performed in the kz−t domain. We examined the feasibility of the L+S method to accurately separate temporally correlated brain background information in the L component while capturing periodic BOLD signals in the S component. We present results acquired in control human volunteers at 3T for both retrospective and prospectively acquired fMRI data for a visual activation block-design task. We show that a SoS fMRI acquisition with an acceleration of four and L+S reconstruction can achieve a brain coverage of 40 slices at 2mm isotropic resolution and 64 x 64 matrix size every 500ms.

Reconstruction of Undersampled Big Dynamic MRI Data Using Non-Convex Low-Rank and Sparsity Constraints.

Dynamic magnetic resonance imaging (MRI) has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t)-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM) is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments.

Dynamic Magnetic Resonance Imaging via Nonconvex Low-Rank Matrix Approximation

Reconstruction of highly accelerated dynamic magnetic resonance imaging (MRI) is of crucial importance for the medical diagnosis. The application of general robust principal component analysis (RPCA) to MRI can increase imaging speed and efficiency. However, conventional RPCA makes use of nuclear norm as convex surrogate of the rank function, whose drawbacks have been mentioned in plenty of literature. Recently, nonconvex surrogates of the rank function in RPCA have been widely investigated and proved to be tighter rank approximation than nuclear norm by the massive experimental results. Motivated by this, we propose a nonconvex alternating direction method based on nonconvex rank approximation to reconstruct dynamic MRI data from undersampled $k-t$ space data. We solve the associated nonconvex model by the alternating direction method and difference of convex programming. The convergence analysis provided guarantees the effectiveness of our algorithm. Experimental results on cardiac perfusion and cardiac cine MRI data demonstrate that our method outperforms the state-of-the-art MRI reconstruction methods in both image clarity and computation efficiency.

A Two-Stage Low Rank Approach for Calibrationless Dynamic Parallel Magnetic Resonance Image Reconstruction

Parallel magnetic resonance imaging (MRI) is an imaging technique by acquiring a reduced amount of data in Fourier domain with multiple receiver coils. To recover the underlying imaging object, one often needs the explicit knowledge of coil sensitivity maps, or some additional fully acquired data blocks called the auto-calibration signals (ACS). In this paper, we show that by exploiting the between-frame redundancy of dynamic parallel MRI data, it is possible to achieve simultaneous coil sensitivity map estimation and image sequence reconstruction. Specially, we introduce a novel two-stage approach for dynamic parallel MRI reconstruction without pre-calibrating the coil sensitivity maps nor additionally acquiring any fully sampled ACS. Numerical experiments demonstrate that, the performance of the proposed approach is better than other state-of-the-art approaches for calibrationless dynamic parallel MRI reconstruction.

Rank-One and Transformed Sparse Decomposition for Dynamic Cardiac MRI.

It is challenging and inspiring for us to achieve high spatiotemporal resolutions in dynamic cardiac magnetic resonance imaging (MRI). In this paper, we introduce two novel models and algorithms to reconstruct dynamic cardiac MRI data from under-sampled k − t space data. In contrast to classical low-rank and sparse model, we use rank-one and transformed sparse model to exploit the correlations in the dataset. In addition, we propose projected alternative direction method (PADM) and alternative hard thresholding method (AHTM) to solve our proposed models. Numerical experiments of cardiac perfusion and cardiac cine MRI data demonstrate improvement in performance.