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Regularization Of Inverse Problems

Purpose To develop and evaluate a novel deep learning-based image reconstruction approach called MANTIS (Model-Augmented Neural neTwork with Incoherent k-space Sampling) for efficient MR parameter mapping. Methods MANTIS combines end-to-end convolutional neural network (CNN) mapping, incoherent k-space undersampling, and a physical model as a synergistic framework. The CNN mapping directly converts a series of undersampled images straight into MR parameter maps using supervised training. Signal model fidelity is enforced by adding a pathway between the undersampled k-space and estimated parameter maps to ensure that the parameter maps produced synthesized k-space consistent with the acquired undersampling measurements. The MANTIS framework was evaluated on the T2 mapping of the knee at different acceleration rates and was compared with 2 other CNN mapping methods and conventional sparsity-based iterative reconstruction approaches. Global quantitative assessment and regional T2 analysis for the cartilage and meniscus were performed to demonstrate the reconstruction performance of MANTIS. Results MANTIS achieved high-quality T2 mapping at both moderate (R = 5) and high (R = 8) acceleration rates. Compared to conventional reconstruction approaches that exploited image sparsity, MANTIS yielded lower errors (normalized root mean square error of 6.1% for R = 5 and 7.1% for R = 8) and higher similarity (structural similarity index of 86.2% at R = 5 and 82.1% at R = 8) to the reference in the T2 estimation. MANTIS also achieved superior performance compared to direct CNN mapping and a 2-step CNN method. Conclusion The MANTIS framework, with a combination of end-to-end CNN mapping, signal model-augmented data consistency, and incoherent k-space sampling, is a promising approach for efficient and robust estimation of quantitative MR parameters.

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MANTIS: Model-Augmented Neural neTwork with Incoherent k-space Sampling for efficient MR parameter mapping.

Purpose
To develop a model-based reconstruction technique for single-shot T1 mapping with high spatial resolution, accuracy, and precision using an inversion-recovery (IR) fast low-angle shot (FLASH) acquisition with radial encoding.

Methods
The proposed model-based reconstruction jointly estimates all model parameters, that is, the equilibrium magnetization, steady-state magnetization, 1/ T1*, and all coil sensitivities from the data of a single-shot IR FLASH acquisition with a small golden-angle radial trajectory. Joint sparsity constraints on the parameter maps are exploited to improve the performance of the iteratively regularized Gauss-Newton method chosen for solving the nonlinear inverse problem. Validations include both a numerical and experimental T1 phantom, as well as in vivo studies of the human brain and liver at 3 T.

Results
In comparison to previous reconstruction methods for single-shot T1 mapping, which are based on real-time MRI with pixel-wise fitting and a model-based approach with a predetermination of coil sensitivities, the proposed method presents with improved robustness against phase errors and numerical precision in both phantom and in vivo studies.

Conclusion
The comprehensive model-based reconstruction with L1 regularization offers rapid and robust T1 mapping with high accuracy and precision. The method warrants accelerated computing and online implementation for extended clinical trials. Magn Reson Med 79:730–740, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Model-based T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH.

Noradrenaline is a neurotransmitter involved in general arousal, selective attention, memory, inflammation, and neurodegeneration. The purpose of this work was to delineate noradrenergic neurons in vivo by T1-weighted MRI with magnetization transfer (MT). In the brainstem of human and mice, MRI identified the locus coeruleus, dorsal motor vagus nucleus, and nucleus tractus solitarius. Given (1) the long T1 and low magnetization transfer ratio for the noradrenergic cell groups compared to other gray matter, (2) significant correlation between MT MRI signal intensity and proton density, and (3) no correlation between magnetization transfer ratio (or R1) and iron, copper, or manganese in human brain, the high MRI signal of the noradrenergic neurons must be attributed to abundant water protons interacting with any T1-shortening paramagnetic ions in active cells rather than to specific T1-shortening molecules. The absence of a high MRI signal from the locus coeruleus of Ear2(-/-) mice lacking noradrenergic neurons confirms that cell bodies of noradrenergic neurons are the source of the bright MRI appearance. The observation of this high signal in DBH(-/-) mice, in 3-week-old mice, and in mice under hyperoxia/hypercapnia/hypoxia together with the general absence of neuromelanin (NM) in noradrenergic neurons of young rodents further excludes that it is due to NM, dopamine β-hydroxylase, their binding to paramagnetic ions, blood inflow, or hemoglobin. Instead, these findings indicate a high density of water protons whose T1 is shortened by paramagnetic ions as the relevant source of the high MRI signal. In the brain of APP/PS1/Ear2(-/-) mice, a transgenic model of Alzheimer's disease, MRI detected noradrenergic neuron loss in the locus coeruleus. Proton magnetic resonance spectroscopy revealed that a 60-75% reduction of noradrenaline is responsible for a reduction of N-acetylaspartate and glutamate in the hippocampus as well as for a shortening of the water proton T2 in the frontal cortex. These results suggest that a concurrent shortage of noradrenaline in Alzheimer's disease accelerates pathologic processes such as inflammation and neuron loss.

/pdf/magnetic-resonance-imaging-of-noradrenergic-neurons-4qsothm5ef.pdf

Magnetic resonance imaging of noradrenergic neurons

Purpose To evaluate the feasibility of using compressed sensing (CS) to accelerate 3D-T1ρ mapping of cartilage and to reduce total scan times without degrading the estimation of T1ρ relaxation times. Methods Fully sampled 3D-T1ρ datasets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared, including finite differences, temporal and spatial wavelets, learned transforms using principal component analysis (PCA) and K-means singular value decomposition (K-SVD), explicit exponential models, low rank and low rank plus sparse models. Spatial filtering prior to T1ρ parameter estimation was also tested. Synthetic phantom (n = 6) and in vivo human knee cartilage datasets (n = 7) were included. Results Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative T1ρ error lower than 4.5%. Some sparsifying transforms, such as spatiotemporal finite difference (STFD), exponential dictionaries (EXP) and low rank combined with spatial finite difference (L+S SFD) significantly improved this performance, reaching average relative T1ρ error below 6.5% on T1ρ relaxation times with AF up to 10, when spatial filtering was used before T1ρ fitting, at the expense of smoothing the T1ρ maps. The STFD achieved 5.1% error at AF = 10 with spatial filtering prior to T1ρ fitting. Conclusion Accelerating 3D-T1ρ mapping of cartilage with CS is feasible up to AF of 10 when using STFD, EXP or L+S SFD regularizers. These three best CS methods performed satisfactorily on synthetic phantom and in vivo knee cartilage for AFs up to 10, with T1ρ error of 6.5%.

Accelerating 3D-T1ρ mapping of cartilage using compressed sensing with different sparse and low rank models.

Purpose
To develop an image noise filter suitable for MRI in real time (acquisition and display), which preserves small isolated details and efficiently removes background noise without introducing blur, smearing, or patch artifacts.

Theory and Methods
The proposed method extends the nonlocal means algorithm to adapt the influence of the original pixel value according to a simple measure for patch regularity. Detail preservation is improved by a compactly supported weighting kernel that closely approximates the commonly used exponential weight, while an oracle step ensures efficient background noise removal. Denoising experiments were conducted on real-time images of healthy subjects reconstructed by regularized nonlinear inversion from radial acquisitions with pronounced undersampling.

Results
The filter leads to a signal-to-noise ratio (SNR) improvement of at least 60% without noticeable artifacts or loss of detail. The method visually compares to more complex state-of-the-art filters as the block-matching three-dimensional filter and in certain cases better matches the underlying noise model. Acceleration of the computation to more than 100 complex frames per second using graphics processing units is straightforward.

Conclusion
The sensitivity of nonlocal means to small details can be significantly increased by the simple strategies presented here, which allows partial restoration of SNR in iteratively reconstructed images without introducing a noticeable time delay or image artifacts. Magn Reson Med 77:1340–1352, 2017. © 2016 International Society for Magnetic Resonance in Medicine

Image denoising for real‐time MRI

OBJECTIVE The aim of this study was to develop a rapid diffusion-weighted (DW) magnetic resonance imaging (MRI) technique for whole-brain studies without susceptibility artifacts and measuring times below 3 minutes. MATERIALS AND METHODS The proposed method combines a DW spin-echo module with a single-shot stimulated echo acquisition mode MRI sequence. Previous deficiencies in image quality due to limited signal-to-noise ratio are compensated for (1) by radial undersampling to enhance the flip angle and thus the signal strength of stimulated echoes; (2) by defining the image reconstruction as a nonlinear inverse problem, which is solved by the iteratively regularized Gauss-Newton method; and (3) by denoising with use of a modified nonlocal means filter. The method was implemented on a 3 T MRI system (64-channel head coil, 80 mT · m gradients) and evaluated for 10 healthy subjects and 2 patients with an ischemic lesion and epidermoid cyst, respectively. RESULTS High-quality mean DW images of the entire brain were obtained by acquiring 1 non-DW image and 6 DW images with different diffusion directions at b = 1000 s · mm. The achievable resolution for a total measuring time of 84 seconds was 1.5 mm in plane with a section thickness of 4 mm (55 sections). A measuring time of 168 seconds allowed for an in-plane resolution of 1.25 mm and a section thickness of 3 mm (54 sections). Apparent diffusion coefficient values were in agreement with literature data. CONCLUSIONS The proposed method for DW MRI offers immunity against susceptibility problems, high spatial resolution, adequate signal-to-noise ratio and clinically feasible scan times of less than 3 minutes for whole-brain studies. More extended clinical trials require accelerated computation and online reconstruction.

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Rapid Diffusion-Weighted Magnetic Resonance Imaging of the Brain Without Susceptibility Artifacts: Single-Shot STEAM With Radial Undersampling and Iterative Reconstruction.

PURPOSE To develop an auto-calibrated image reconstruction for highly accelerated multi-directional phase-contrast (PC) MRI that compensates for (1) reconstruction instabilities occurring for phase differences near ±π and (2) phase errors by concomitant magnetic fields that differ for individual radial spokes. THEORY AND METHODS A model-based image reconstruction for real-time PC MRI based on nonlinear inversion is extended to multi-directional flow by exploiting multiple flow-encodings for the estimation of velocity vectors. An initial smoothing constraint during iterative optimization is introduced to resolve the ambiguity of the solution space by penalizing phase wraps. Maxwell terms are considered as part of the signal model on a line-by-line basis to address phase errors by concomitant magnetic fields. The reconstruction methods are evaluated using simulated data and cross-sectional imaging of a rotating-disc, as well as in vivo for the aortic arch and cervical spinal canal at 3T. RESULTS Real-time three-directional velocity mapping in the aortic arch is achieved at 1.8 × 1.8 × 6 mm3 spatial and 60 ms temporal resolution. Artificial phase wraps are avoided in all cases using the smoothness constraint. Inter-spoke differences of concomitant magnetic fields are effectively compensated for by the model-based image reconstruction with integrated radial Maxwell correction. CONCLUSION Velocity vector reconstructions based on nonlinear inversion allow for high degrees of radial data undersampling paving the way for multi-directional PC MRI in real time. Whether a spoke-wise treatment of Maxwell terms is required or a computationally cheaper frame-wise approach depends on the individual application.

Jakob Klosowski

Papers

Model-based T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH.

Image denoising for real‐time MRI

Rapid Diffusion-Weighted Magnetic Resonance Imaging of the Brain Without Susceptibility Artifacts: Single-Shot STEAM With Radial Undersampling and Iterative Reconstruction.

Velocity vector reconstruction for real-time phase-contrast MRI with radial Maxwell correction.