Compressive manifold learning: Estimating one-dimensional respiratory motion directly from undersampled k-space data

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

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.

Purpose: To evaluate the feasibility of using the weighted hybrid iterative spiral k-space encoded estimation (WHISKEE) technique to improve spatial resolution of tracking images for onboard MR image guided radiation therapy (MR-IGRT). Methods: MR tracking images of abdomen and pelvis had been acquired from healthy volunteers using the ViewRay onboard MRIGRT system (ViewRay Inc. Oakwood Village, OH) at a spatial resolution of 2.0mm*2.0mm*5.0mm. The tracking MR images were acquired using the TrueFISP sequence. The temporal resolution had to be traded off to 2 frames per second (FPS) to achieve the 2.0mm in-plane spatial resolution. All MR images were imported into the MATLAB software. K-space data were synthesized through the Fourier Transform of the MR images. A mask was created to selected k-space points that corresponded to the under-sampled spiral k-space trajectory with an acceleration (or undersampling) factor of 3. The mask was applied to the fully sampled k-space data to synthesize the undersampled k-space data. The WHISKEE method was applied to the synthesized undersampled k-space data to reconstructed tracking MR images at 6 FPS. As a comparison, the undersampled k-space data were also reconstructed using the zero-padding technique. The reconstructed images were compared to the original image. The relatively reconstructionmore » error was evaluated using the percentage of the norm of the differential image over the norm of the original image. Results: Compared to the zero-padding technique, the WHISKEE method was able to reconstruct MR images with better image quality. It significantly reduced the relative reconstruction error from 39.5% to 3.1% for the pelvis image and from 41.5% to 4.6% for the abdomen image at an acceleration factor of 3. Conclusion: We demonstrated that it was possible to use the WHISKEE method to expedite MR image acquisition for onboard MR-IGRT systems to achieve good spatial and temporal resolutions simultaneously. Y. Hu and O. green receive travel reimbursement from ViewRay. S. Mutic has consulting and research agreements with ViewRay. Q. Zeng, R. Nana, J.L. Patrick, S. Shvartsman and J.F. Dempsey are ViewRay employees.« less

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)

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.

Using High-Pass Filter to Enhance Scan Specific Learning for MRI Reconstruction without Any Extra Training Data

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. .

The aim of this study was to implement and evaluate an accelerated three-dimensional (3D) cine phase contrast MRI sequence by combining a randomly sampled 3D k-space acquisition sequence with an echo planar imaging (EPI) readout. An accelerated 3D cine phase contrast MRI sequence was implemented by combining EPI readout with randomly undersampled 3D k-space data suitable for compressed sensing (CS) reconstruction. The undersampled data were then reconstructed using low-dimensional structural self-learning and thresholding (LOST). 3D phase contrast MRI was acquired in 11 healthy adults using an overall acceleration of 7 (EPI factor of 3 and CS rate of 3). For comparison, a single two-dimensional (2D) cine phase contrast scan was also performed with sensitivity encoding (SENSE) rate 2 and approximately at the level of the pulmonary artery bifurcation. The stroke volume and mean velocity in both the ascending and descending aorta were measured and compared between two sequences using Bland-Altman plots. An average scan time of 3 min and 30 s, corresponding to an acceleration rate of 7, was achieved for 3D cine phase contrast scan with one direction flow encoding, voxel size of 2 × 2 × 3 mm(3) , foot-head coverage of 6 cm and temporal resolution of 30 ms. The mean velocity and stroke volume in both the ascending and descending aorta were statistically equivalent between the proposed 3D sequence and the standard 2D cine phase contrast sequence. The combination of EPI with a randomly undersampled 3D k-space sampling sequence using LOST reconstruction allows a seven-fold reduction in scan time of 3D cine phase contrast MRI without compromising blood flow quantification.

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.

Motivation: Long scan time of phase sensitive inversion recovery (PSIR) for cardiac late gadolinium enhancement imaging significantly hinders the widespread applications of time-sensitive clinical scenarios. Goal(s): This study aims to accelerate PSIR acquisition and enhance reconstruction performance using deep equilibrium models. Approach: To reduce cardiac motion-induced blurring, segmented undersampled PSIR k-space data was divided into multiple shots instead of a single dataset. Using a deep learning approach with deep equilibrium models, dynamic inversion recovery and proton density reference images were reconstructed from each shot's highly undersampled k-space data. Results: This approach enables accurate dynamic PSIR image reconstruction with acceleration rates up to 12.5. Impact: The proposed method could greatly reduce the scan time of PSIR data acquisition and achieve high quality images, therefore has a broad spectrum of potential clinical applications.

In this paper, a novel magnetic resonance (MR) images reconstruction framework based on paired dictionary learning (PDL) is proposed by jointly training two dictionaries for both undersampled k-space data and fully sampled k-space data. We find an optimal sparse representation for each undersampled k-space patch of the input MR image, and then utilize these representation coeffificients and fully sampled k-space patch dictionary to reconstruct the MR image. Two undersampling schemes and different sampling rates are applied to verify the performance of the proposed method. Experiments on brain images data set show that the proposed PDL algorithm can achieve higher structural similarity measure (SSIM) and lower relative l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> norm error (RLNE), meanwhile, it is superior to classical compressed sensing MRI (CS-MRI) methods on suppressing image artifacts and retaining image edge details.

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.

To present and validate a manifold learning (ML)-based method that can estimate both cardiac and respiratory navigator signals from electrocardiogram (ECG)-free free-breathing cardiac magnetic resonance imaging (MRI) data to achieve self-gated retrospective CINE reconstruction. In this work the use of the ML method is demonstrated for 2D cardiac CINE to achieve both cardiac and respiratory self-gating without the need of an external navigator or ECG signal. This is achieved by sequentially applying ML to two sets of retrospectively reconstructed real-time images with differing temporal resolutions. A 1D cardiac signal is estimated by applying ML to high temporal resolution real-time images reconstructed from the acquired data. Using the estimated cardiac signal, a 1D respiratory signal was obtained by applying the ML method to low temporal resolution images reconstructed from the same acquired data for each cardiac cycle. Data were acquired in five volunteers with a 2D golden angle radial trajectory in a balanced steady-state free precession (b-SSFP) acquisition. The accuracy of the estimated cardiac signal was calculated as the standard deviation of the temporal difference between the estimated signal and the recorded ECG. The correlation between the estimated respiratory signal and standard pencil beam navigator signal was evaluated. Gated CINE reconstructions (20 cardiac phases per cycle, temporal resolution ∼30 msec) using the estimated cardiac and respiratory signals were qualitatively compared against conventional ECG-gated breath-hold CINE acquisitions. Accurate cardiac signals were estimated with the proposed method, with an error standard deviation in comparison to ECG lower than 20 msec. Respiratory signals estimated with the proposed method achieved a mean cross-correlation of 94% with respect to standard pencil beam navigator signals. Good quality visual scores of 2.80 ± 0.45 (scores from 0, bad, to 4, excellent quality) were observed for the proposed approach in comparison with the conventional ECG-gated breath-hold images (visual score: 3.00 ± 0.71). Accurate respiratory and cardiac navigator signals can be estimated using the proposed framework from the acquired data itself, resulting in retrospective self-gated CINE reconstruction with high spatial and temporal quality.

To develop a three-dimensional (3D) free-breathing myocardial T1 mapping sequence for assessment of left ventricle diffuse fibrosis after contrast administration. In the proposed sequence, multiple 3D inversion recovery images are acquired in an interleaved manner. A mixed prospective/retrospective navigator scheme is used to obtain the 3D Cartesian k-space data with fully sampled center and randomly undersampled outer k-space. The resulting undersampled 3D k-space data are then reconstructed using compressed sensing. Subsequently, T1 maps are generated by voxel-wise curve fitting of the individual interleaved images. In a phantom study, the accuracy of the 3D sequence was evaluated against two-dimensional (2D) modified Look-Locker inversion recovery (MOLLI) and spin-echo sequences. In vivo T1 times of the proposed method were compared with 2D multislice MOLLI T1 mapping. Subsequently, the feasibility of high-resolution 3D T1 mapping with spatial resolution of 1.7 × 1.7 × 4 mm(3) was demonstrated. The proposed method shows good agreement with 2D MOLLI and the spin-echo reference in phantom. No significant difference was found in the in vivo T1 times estimated using the proposed sequence and the 2D MOLLI technique (myocardium, 330 ± 66 ms versus 319 ± 93 ms; blood pools, 211 ± 68 ms versus 210 ± 98 ms). However, improved homogeneity, as measured using standard deviation of the T1 signal, was observed in the 3D T1 maps. The proposed sequence enables high-resolution 3D T1 mapping after contrast injection during free-breathing with volumetric left ventricle coverage.

Multi-contrast magnetic resonance imaging (MRI) is widely used in clinical diagnosis. However, it is time-consuming to obtain MR data of multi-contrasts and the long scanning time may bring unexpected physiological motion artifacts. To obtain MR images of higher quality within limited acquisition time, we propose an effective model to reconstruct images from under-sampled k-space data of one contrast by utilizing another fully-sampled contrast of the same anatomy. Specifically, multiple contrasts from the same anatomical section exhibit similar structures. Enlightened by the fact that co-support of an image provides an appropriate characterization of morphological structures, we develop a similarity regularization of the co-supports across multi-contrasts. In this case, the guided MRI reconstruction problem is naturally formulated as a mixed integer optimization model consisting of three terms, the data fidelity of k-space, smoothness-enforcing regularization, and co-support regularization. An effective algorithm is developed to solve this minimization model alternatively. In the numerical experiments, T2-weighted images are used as the guidance to reconstruct T1-weighted/T2-weighted-Fluid-Attenuated Inversion Recovery (T2-FLAIR) images and PD-weighted images are used as the guidance to reconstruct PDFS-weighted images, respectively, from their under-sampled k-space data. The experimental results demonstrate that the proposed model outperforms other state-of-the-art multi-contrast MRI reconstruction methods in terms of both quantitative metrics and visual performance at various sampling ratios.