GESPIRiT: ESPIRiT combined with GRAPPA while autocalibration data is insufficient

Integrated variable projection approach (IVAPA) for parallel magnetic resonance imaging

Magnetic resonance imaging (MRI) has an important feature that it provides multiple images with different contrasts for complementary diagnostic information. However, a large amount of data is needed for multi-contrast images depiction, and thus, the scan is time-consuming. Many methods based on parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) are applied to accelerate multi-contrast MR imaging. Nevertheless, the image reconstructed by sophisticated pMRI methods contains residual aliasing artifact that degrades the quality of the image when the acceleration factor is high. Other methods based on CS always suffer the regularization parameter-selecting problem. To address these issues, a new method is presented for joint multi-contrast image reconstruction and coil sensitivity estimation. The coil sensitivities can be shared during the reconstruction due to the identity of coil sensitivity profiles of different contrast images for imaging stationary tissues. The proposed method uses the coil sensitivities as sharable information during the reconstruction to improve the reconstruction quality. As a result, the residual aliasing artifact can be effectively removed in the reconstructed multi-contrast images even if the acceleration factor is high. Besides, as there is no regularization term in the proposed method, the troublesome regularization parameter selection in the CS can also be avoided. Results from multi-contrast in vivo experiments demonstrated that multi-contrast images can be jointly reconstructed by the proposed method with effective removal of the residual aliasing artifact at a high acceleration factor.

The image quality of iterative self-consistent parallel imaging reconstruction (SPIRiT) algorithm highly depends on the accuracy of linear coefficients which can be easily influenced by k-space noise. In this study, an improved calibration framework for SPIRiT is presented to reduce noise-induced errors and to adaptively generate optimal linear weighting coefficients. Specifically, the auto-calibration signals (ACS) are first mapped to a high-dimensional feature space through a polynomial mapping, and the optimal coefficients are adaptively obtained in this new feature space with discrepancy-based Tikhonov regularization and then truncated for SPIRiT reconstruction. Phantom and in vivo brain reconstruction were, respectively, performed and this calibration framework was mainly evaluated in Cartesian k-space-based SPIRiT reconstruction. In both phantom and in vivo reconstructions, noise-induced errors can be reduced by polynomial mapping and optimal regularization parameter, which improves the accuracy of linear coefficients. Both qualitative and quantitative results demonstrated that the proposed calibration framework resulted in better image quality without loss of resolution compared with the conventional calibration at different acceleration factors. The proposed calibration framework can effectively improve SPIRiT image quality.

In this paper, we propose a novel approach called robust iterative self-consistent parallel imaging reconstruction (RSPIRiT) in parallel magnetic resonance imaging (pMRI). Different from the smooth Tikhonov regularization used in SPIRiT, our model utilizes generalized Lasso to fix calibration errors in the reconstruction process. It results in a non-smooth optimization problem, which we introduce a new primal-dual pMRI algorithm to solve. We conduct extensive experiments to demonstrate the effectiveness of our approach, compared to state-of-the-art methods.

SPIRiT (iterative self-consistent parallel imaging reconstruction), and its sparsity-regularized variant L1-SPIRiT, are compatible with both Cartesian and non-Cartesian magnetic resonance imaging sampling trajectories. However, the non-Cartesian framework is more expensive computationally, involving a nonuniform Fourier transform with a nontrivial Gram matrix. We propose a novel implementation of the regularized reconstruction problem using variable splitting, alternating minimization of the augmented Lagrangian, and careful preconditioning. Our new method based on the alternating direction method of multipliers converges much faster than existing methods because of the preconditioners' heightened effectiveness. We demonstrate such rapid convergence substantially improves image quality for a fixed computation time. Our framework is a step forward towards rapid non-Cartesian L1-SPIRiT reconstructions.

Simultaneous multi-slice (SMS) bSSFP imaging enables stress myocardial perfusion imaging with high spatial resolution and increased spatial coverage. Standard parallel imaging techniques (e.g., TGRAPPA) can be used for image reconstruction but result in high noise level. Alternatively, iterative reconstruction techniques based on temporal regularization (ITER) improve image quality but are associated with reduced temporal signal fidelity and long computation time limiting their online use. The aim is to develop an image reconstruction technique for SMS-bSSFP myocardial perfusion imaging combining parallel imaging and image-based denoising using a novel noise map estimation network (NoiseMapNet), which preserves both sharpness and temporal signal profiles and that has low computational cost. The proposed reconstruction of SMS images consists of a standard temporal parallel imaging reconstruction (TGRAPPA) with motion correction (MOCO) followed by image denoising using NoiseMapNet. NoiseMapNet is a deep learning network based on a 2D Unet architecture and aims to predict a noise map from an input noisy image, which is then subtracted from the noisy image to generate the denoised image. This approach was evaluated in 17 patients who underwent stress perfusion imaging using a SMS-bSSFP sequence. Images were reconstructed with (a) TGRAPPA with MOCO (thereafter referred to as TGRAPPA), (b) iterative reconstruction with integrated motion compensation (ITER), and (c) proposed NoiseMapNet-based reconstruction. Normalized mean squared error (NMSE) with respect to TGRAPPA, myocardial sharpness, image quality, perceived SNR (pSNR), and number of diagnostic segments were evaluated. NMSE of NoiseMapNet was lower than using ITER for both myocardium (0.045 ± 0.021 vs. 0.172 ± 0.041, p < 0.001) and left ventricular blood pool (0.025 ± 0.014 vs. 0.069 ± 0.020, p < 0.001). There were no significant differences between all methods for myocardial sharpness (p = 0.77) and number of diagnostic segments (p = 0.36). ITER led to higher image quality than NoiseMapNet/TGRAPPA (2.7 ± 0.4 vs. 1.8 ± 0.4/1.3 ± 0.6, p < 0.001) and higher pSNR than NoiseMapNet/TGRAPPA (3.0 ± 0.0 vs. 2.0 ± 0.0/1.3 ± 0.6, p < 0.001). Importantly, NoiseMapNet yielded higher pSNR (p < 0.001) and image quality (p < 0.008) than TGRAPPA. Computation time of NoiseMapNet was only 20s for one entire dataset. NoiseMapNet-based reconstruction enables fast SMS image reconstruction for stress myocardial perfusion imaging while preserving sharpness and temporal signal profiles.

Several magnetic resonance parallel imaging techniques require explicit estimates of the receive coil sensitivity profiles. These estimates must be accurate over both the object and its surrounding regions to avoid generating artifacts in the reconstructed images. Regularized estimation methods that involve minimizing a cost function containing both a data-fit term and a regularization term provide robust sensitivity estimates. However, these methods can be computationally expensive when dealing with large problems. In this paper, we propose an iterative algorithm based on variable splitting and the augmented Lagrangian method that estimates the coil sensitivity profile by minimizing a quadratic cost function. Our method, ADMM-Circ, reformulates the finite differencing matrix in the regularization term to enable exact alternating minimization steps. We also present a faster variant of this algorithm using intermediate updating of the associated Lagrange multipliers. Numerical experiments with simulated and real data sets indicate that our proposed method converges approximately twice as fast as the preconditioned conjugate gradient method over the entire field-of-view. These concepts may accelerate other quadratic optimization problems.

Parallel magnetic resonance imaging (MRI) techniques use spatial information from arrays of radiofrequency (RF) detector coils to accelerate imaging. A number of parallel MRI techniques have been described in recent years, and numerous clinical applications are currently being explored. The advent of practical parallel imaging presents various challenges for image reconstruction and RF system design. Recent advances in tailored SiMultaneous Acquisition of Spatial Harmonics (SMASH) image reconstructions are summarized. These advances enable robust SMASH imaging in arbitrary image planes with a wide range of coil array geometries. A generalized formalism is described which may be used to understand the relations between SMASH and SENSE, to derive typical implementations of each as special cases, and to form hybrid techniques combining some of the advantages of both. Accurate knowledge of coil sensitivities is crucial for parallel MRI, and errors in calibration represent one of the most common and the most pernicious sources of error in parallel image reconstructions. As one example, motion of the patient and/or the coil array between the sensitivity reference scan and the accelerated acquisition can lead to calibration errors and reconstruction artifacts. Self-calibrating parallel MRI approaches that address this problem by eliminating the need for external sensitivity references are reviewed. The ultimate achievable signal-to-noise ratio (SNR) for parallel MRI studies is closely tied to the geometry and sensitivity patterns of the coil arrays used for spatial encoding. Several parallel imaging array designs that depart from the traditional model of overlapped adjacent loop elements are described.

In clinical exams, multi-contrast images from conventional MRI are scanned with the same field of view (FOV) for complementary diagnostic information, such as proton density- (PD-), T1- and T2-weighted images. Their sharable information can be utilized for more robust and accurate image reconstruction. In this work, we propose a novel model and an efficient algorithm for joint image reconstruction and coil sensitivity estimation in multi-contrast partially parallel imaging (PPI) in MRI. Our algorithm restores the multi-contrast images by minimizing an energy function consisting of an L2-norm fidelity term to reduce construction errors caused by motion, a regularization term of underlying images to preserve common anatomical features by using vectorial total variation (VTV) regularizer, and updating sensitivity maps by Tikhonov smoothness based on their physical property. We present the numerical results including T1- and T2-weighted MR images recovered from partially scanned k-space data and provide the comparisons between our results and those obtained from the related existing works. Our numerical results indicate that the proposed method using vectorial TV and penalties on sensitivities can be made promising and widely used for multi-contrast multi-channel MR image reconstruction.

The rotating Cartesian k-space multiphase steady-state imaging with contrast (ROCK-MUSIC) pulse sequence enables acquisition of whole-heart, cardiac phase-resolved images in pediatric congenital heart disease (CHD) without reliance on the ventilator gating signal. Multidimensional reconstruction with low rank tensor (LRT) has shown promise for resolving complex cardiorespiratory motion. To enhance ROCK-MUSIC by resolving cardiorespiratory phases using LRT reconstruction and to enable semi-automatic hyperparameter tuning by developing an image quality scoring model. Retrospective. Thirty patients (45% female, age 2 days to 6.7 years) with CHD. 3-T, four-dimensional (4D) spoiled gradient recalled echo sequence. Eigenvector-based iTerative Self-consistent Parallel Imaging Reconstruction (ESPIRiT) served as the reference comparison for LRT reconstruction. A 4-point Likert scale was used for cardiac and vascular image quality scoring based on cardiac chamber definition, lumen signal uniformity, vascular margin clarity, and motion artifact. Ejection fraction and ventricular volumes were assessed in 16 patients. Signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and edge sharpness were computed. Intraclass correlation coefficients, Wilcoxon signed-rank test, Bland-Altman. A P-value <0.05 was considered statistically significant. Relative to ESPIRiT, LRT images received significantly higher cardiac (2.81 ± 0.57 vs. 3.19 ± 0.54) and vascular (2.81 ± 0.60 vs. 3.36 ± 0.53) image quality scores. Image quality scoring with semi-automated hyperparameter tuning showed strong correlations (R2 = 0.748) among image quality, SNR, and septal sharpness. Comparison of ejection fraction and volumetry derived from ESPIRiT, and LRT showed no significant systematic difference (P = 0.32). Integration of low-rank reconstruction with ROCK-MUSIC acquisition may be feasible, and semi-automatic hyperparameter tuning could be effective for generating cardiorespiratory resolved images. 2 TECHNICAL EFFICACY: Stage 1.

We consider the problem of estimating receiver coil sensitivity functions in parallel MRI. By exploiting the multichannel nature of the problem, where multiple acquisitions of the same image function are obtained with different sensitivity weightings, we obtain a subspace-based framework for directly solving for the sensitivity functions. The proposed approach does not rely on the sum-of-squares assumption used in existing estimation schemes; this assumption tends to be violated towards the center of the image, thus leading to errors in the sensitivity estimates. Our approach eliminates this problem, producing superior sensitivity estimates in comparison to the sum-of-squares technique. In addition, the proposed restoration procedure is non-iterative, computationally efficient, and applicable both to cases where pilot scans are available or where auto-calibration data are collected with each scan. We present experimental results using actual and simulated data to assess the performance of our approach in comparison with existing methods

Spiral MRI has received increasing attention due to its reduced T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> *-decay and robustness against bulk physiologic motion. In parallel imaging, spiral trajectories are especially of great interest due to their inherent self-calibration capabilities, which is especially useful for dynamic imaging applications such as fMRI and cardiac imaging. The existing self-calibration techniques for spiral use the k-space center data that are sampled densely in the accelerated acquisition for coil sensitivity estimation. There exists a trade-off in choosing the radius of the center data: it must be sufficiently large to contain all major spatial frequencies of coil sensitivity, but not too large to cause significant aliasing artifacts due to undersampling below Nyquist rate as the trajectory moves away from the center k-space. To address this tradeoff, we generalize the JSENSE approach, which has demonstrated success in Cartesian case, to spiral trajectory. Specifically, the method jointly estimates the coil sensitivities and reconstructs the desired image through cross validations so that the sensitivities are estimated from the full data recovered by SENSE instead of the center k-space data only, thereby increasing high frequency information without introducing aliasing artifacts. We use experimental results to show the proposed method improves sensitivities, which leads to a more accurate SENSE reconstruction

The use of self-calibrating techniques in parallel magnetic resonance imaging eliminates the need for coil sensitivity calibration scans and avoids potential mismatches between calibration scans and subsequent accelerated acquisitions (e.g., as a result of patient motion). Most examples of self-calibrating Cartesian parallel imaging techniques have required the use of modified k-space trajectories that are densely sampled at the center and more sparsely sampled in the periphery. However, spiral and radial trajectories offer inherent self-calibrating characteristics because of their densely sampled center. At no additional cost in acquisition time and with no modification in scanning protocols, in vivo coil sensitivity maps may be extracted from the densely sampled central region of k-space. This work demonstrates the feasibility of self-calibrated spiral and radial parallel imaging using a previously described iterative non-Cartesian sensitivity encoding algorithm.

To develop a truly calibrationless reconstruction method that derives An Eigenvalue Approach to Autocalibrating Parallel MRI (ESPIRiT) maps from uniformly-undersampled multi-channel MR data by deep learning. ESPIRiT, one commonly used parallel imaging reconstruction technique, forms the images from undersampled MR k-space data using ESPIRiT maps that effectively represents coil sensitivity information. Accurate ESPIRiT map estimation requires quality coil sensitivity calibration or autocalibration data. We present a U-Net based deep learning model to estimate the multi-channel ESPIRiT maps directly from uniformly-undersampled multi-channel multi-slice MR data. The model is trained using fully-sampled multi-slice axial brain datasets from the same MR receiving coil system. To utilize subject-coil geometric parameters available for each dataset, the training imposes a hybrid loss on ESPIRiT maps at the original locations as well as their corresponding locations within the standard reference multi-slice axial stack. The performance of the approach was evaluated using publicly available T1-weighed brain and cardiac data. The proposed model robustly predicted multi-channel ESPIRiT maps from uniformly-undersampled k-space data. They were highly comparable to the reference ESPIRiT maps directly computed from 24 consecutive central k-space lines. Further, they led to excellent ESPIRiT reconstruction performance even at high acceleration, exhibiting a similar level of errors and artifacts to that by using reference ESPIRiT maps. A new deep learning approach is developed to estimate ESPIRiT maps directly from uniformly-undersampled MR data. It presents a general strategy for calibrationless parallel imaging reconstruction through learning from the coil and protocol-specific data.

A variational approach to magnetic resonance coil sensitivity estimation