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Unrolled Neural Networks (NNs) have been extensively applied to different image reconstruction problems across all imaging modalities. A key component of the latter is that they allow for physics-informed learning of the regularization method which is parametrized by the NN. However, due to the lack of understanding of deep NNs from a theoretical point of view, unrolled NNs are still black-boxes when the regularizers are given by deep NNs, e.g. U-Nets.Dictionary Learning (DL) is a well-established regularization method which is based on learning a transform to sparsely approximate the signals of interest. Typically, DL-based image reconstruction either employs a dictionary which was pre-trained on a set of patches which were extracted from ground-truth images or a dictionary which is jointly trained during the reconstruction. However, in both cases, the used DL-algorithms are not designed to take into account the reconstruction problem or the underlying physical model which describes the imaging process. In this work, we propose a DL-algorithm based on unrolled NNs to overcome these limitations.We construct an unrolled NN which corresponds to an unrolled DL-based reconstruction algorithm and train the unrolled NN to optimize its weights, i.e. the atoms of the dictionary, by back-propagation in a supervised manner. Further, we propose a new way to employ a 2D dictionary in the spatio-temporal domain. We tested and evaluated the method on an accelerated cardiac cine MR image reconstruction problem using 216/36/36 dynamic images for training, validation and testing and compared it to two well-known state-of-the-art approaches for cardiac cine MRI based on deep iterative CNNs. Further, we analyze the obtained dictionaries in terms of dictionary-coherence and structure of the atoms. Last, we compare the reported methods in terms of stability by applying them to an entirely different dataset consisting of 49 different test images.The investigated physics-informed DL-approach yields significantly more accurate reconstructions compared to the DL-method which uses dictionaries obtained by decoupled pre-training, thereby providing an improvement of up to 4.90 dB in terms of PSNR and 5% in terms of SSIM. Further, the proposed spatio-temporal 2D dictionary outperforms the 1D and 3D dictionaries by preventing smoothing of image details while still accurately removing undersampling artefacts and noise resulting in an increase of up to 1.10 dB in terms of PSNR and 4% in terms of SSIM. Although being surpassed by the CNNs on the first dataset, the proposed NNs-based DL-method is more stable compared to the latter approach and yields comparable results on the second dataset. Last, it has the advantage of being entirely interpretable in each component.The presented physics-informed NN can be used as training algorithm for a classical and interpretable data-driven regularization method based a learned dictionary which can then not only be linked to the considered data but also to the reconstruction method that the NN defines. This article is protected by copyright. All rights reserved.

Objective. To provide 3D high-resolution cardiac T1 maps using model-based super-resolution reconstruction (SRR). Approach. Due to signal-to-noise ratio limitations and the motion of the heart during imaging, often 2D T1 maps with only low through-plane resolution (i.e. slice thickness of 6–8 mm) can be obtained. Here, a model-based SRR approach is presented, which combines multiple stacks of 2D acquisitions with 6–8 mm slice thickness and generates 3D high-resolution T1 maps with a slice thickness of 1.5–2 mm. Every stack was acquired in a different breath hold (BH) and any misalignment between BH was corrected retrospectively. The novelty of the proposed approach is the BH correction and the application of model-based SRR on cardiac T1 Mapping. The proposed approach was evaluated in numerical simulations and phantom experiments and demonstrated in four healthy subjects. Main results. Alignment of BH states was essential for SRR even in healthy volunteers. In simulations, respiratory motion could be estimated with an RMS error of 0.18 ± 0.28 mm. SRR improved the visualization of small structures. High accuracy and precision (average standard deviation of 69.62 ms) of the T1 values was ensured by SRR while the detectability of small structures increased by 40%. Significance. The proposed SRR approach provided T1 maps with high in-plane and high through-plane resolution (1.3 × 1.3 × 1.5–2 mm3). The approach led to improvements in the visualization of small structures and precise T1 values.

Assess and optimise acquisition parameters for continuous cardiac Magnetic Resonance Fingerprinting (MRF).Different acquisition schemes (flip angle amplitude, lobe size, T2-preparation pulses) for cardiac MRF were assessed in simulations and phantom and demonstrated in one healthy volunteer. Three different experimental designs were evaluated using central composite and fractional factorial designs. Relative errors for T1 and T2 were calculated for a wide range of realistic T1 and T2 value combinations. The effect of different designs on the accuracy of T1 and T2 was assessed using response surface modelling and Cohen's f calculations.Larger flip angle amplitudes lead to an improvement of T2 accuracy and precision for simulations and phantom experiments. Similar effects could also be shown qualitatively in in-vivo scans. Accuracy and precision of T1 were robust to different design parameters with improved values for faster flip angle variation. Cohen's f showed that T2-preparation pulses influence the accuracy of T2. The number of pulses used is the most important parameter. Without T2-preparation pulses, RMSE were 3.0 ± 8.09 % for T1 and 16.24 ± 14.47 % for T2. Using those pulses reduced the RMSE to 2.3 ± 8.4 % for T1 and 14.11 ± 13.46 % for T2. Nonetheless, even if the improvement is significant, RMSE are still too high for reliable quantification.In contrast to previous study using triggered MRF sequences using 30° flip angles, large flip angle amplitudes led to better results for continuous cardiac MRF sequences. T2-preparation pulse can improve the accuracy of T2 estimation but lead to longer scan times.

Objective To provide respiratory motion correction for free-breathing myocardial T1 mapping using a pilot tone (PT) and a continuous golden-angle radial acquisition. Materials and methods During a 45 s prescan the PT is acquired together with a dynamic sagittal image covering multiple respiratory cycles. From these images, the respiratory heart motion in head-feet and anterior–posterior direction is estimated and two linear models are derived between the PT and heart motion. In the following scan through-plane motion is corrected prospectively with slice tracking based on the PT. In-plane motion is corrected for retrospectively. Our method was evaluated on a motion phantom and 11 healthy subjects. Results Non-motion corrected measurements using a moving phantom showed T1 errors of 14 ± 4% (p p p Discussion Our proposed PT-based motion correction approach allows for T1 mapping during free-breathing with the same accuracy as a corresponding breathhold T1 mapping scan.

Objective. T1 mapping of the liver is time consuming and can be challenging due to respiratory motion. Here we present a prospective slice tracking approach, which utilizes an external ultra-wide band radar signal and allows for efficient T1 mapping during free-breathing. Approach. The fast radar signal is calibrated to an MR-based motion signal to create a motion model. This motion model provides motion estimates, which are used to carry out slice tracking for any subsequent clinical scan. This approach was evaluated in simulations, phantom experiments and in vivo scans. Main results. Radar-based slice tracking was implemented on an MR system with a total latency of 77 ms. Moving phantom experiments showed accurate motion prediction with an error of 0.12 mm in anterior-posterior and 0.81 mm in head-feet direction. The model error remained stable for up to two hours. In vivo experiments showed visible image improvement with a motion model error three times smaller than with a respiratory bellow. For T1 mapping during free-breathing the proposed approach provided similar results compared to reference T1 mapping during a breathhold. Significance. The proposed radar-based approach achieves accurate slice tracking and enables efficient T1 mapping of the liver during free-breathing. This motion correction approach is independent from scanning parameters and could also be used for applications like MR guided radiotherapy or MR Elastography.

Purpose: Respiratory motion‐compensated (MC) 3D cardiac fat‐water imaging at 7T. Methods: Free‐breathing bipolar 3D triple‐echo gradient‐recalled‐echo (GRE) data with radial phase‐encoding (RPE) trajectory were acquired in 11 healthy volunteers (7M\4F, 21–35 years, mean: 30 years) with a wide range of body mass index (BMI; 19.9–34.0 kg/m2) and volunteer tailored B1+ shimming. The bipolar‐corrected triple‐echo GRE‐RPE data were binned into different respiratory phases (self‐navigation) and were used for the estimation of non‐rigid motion vector fields (MF) and respiratory resolved (RR) maps of the main magnetic field deviations (ΔB0). RR ΔB0 maps and MC ΔB0 maps were compared to a reference respiratory phase to assess respiration‐induced changes. Subsequently, cardiac binned fat‐water images were obtained using a model‐based, respiratory motion‐corrected image reconstruction. Results: The 3D cardiac fat‐water imaging at 7T was successfully demonstrated. Local respiration‐induced frequency shifts in MC ΔB0 maps are small compared to the chemical shifts used in the multi‐peak model. Compared to the reference exhale ΔB0 map these changes are in the order of 10 Hz on average. Cardiac binned MC fat‐water reconstruction reduced respiration induced blurring in the fat‐water images, and flow artifacts are reduced in the end‐diastolic fat‐water separated images. Conclusion: This work demonstrates the feasibility of 3D fat‐water imaging at UHF for the entire human heart despite spatial and temporal B1+ and B0 variations, as well as respiratory and cardiac motion.

PURPOSE: Myocardial fat infiltrations are associated with a range of cardiomyopathies. The purpose of this study was to perform cardio-respiratory motion-correction for model-based water-fat separation to image fatty infiltrations of the heart in a free-breathing, non-cardiac-triggered high-resolution 3D MRI acquisition. METHODS: Data were acquired in nine patients using a free-breathing, non-cardiac-triggered high-resolution 3D Dixon gradient-echo sequence and radial phase encoding trajectory. Motion correction was combined with a model-based water-fat reconstruction approach. Respiratory and cardiac motion models were estimated using a dual-mode registration algorithm incorporating both motion-resolved water and fat information. Qualitative comparisons of fat structures were made between 2D clinical routine reference scans and reformatted 3D motion-corrected images. To evaluate the effect of motion correction the local sharpness of epicardial fat structures was analyzed for motion-averaged and motion-corrected fat images. RESULTS: The reformatted 3D motion-corrected reconstructions yielded qualitatively comparable fat structures and fat structure sharpness in the heart as the standard 2D breath-hold. Respiratory motion correction improved the local sharpness on average by 32% ± 24% with maximum improvements of 81% and cardiac motion correction increased the sharpness further by another 15% ± 11% with maximum increases of 31%. One patient showed a fat infiltration in the myocardium and cardio-respiratory motion correction was able to improve its visualization in 3D. CONCLUSION: The 3D water-fat separated cardiac images were acquired during free-breathing and in a clinically feasible and predictable scan time. Compared to a motion-averaged reconstruction an increase in sharpness of fat structures by 51% ± 27% using the presented motion correction approach was observed for nine patients.

Magnetic resonance imaging (MRI) is a medical imaging technique which is widely used in clinical routine. Standard imaging methods lead to so-called contrast-weighted images. The contrast arises from several tissue-related parameters such as the relaxation times T 1 and T 2. The aim in quantitative MRI (qMRI) is an estimation of these quantitative parameters. Magnetic resonance fingerprinting (MRF) is a promising technique in qMRI that allows for the simultaneous determination of multiple tissue-related parameters within a short acquisition time. The conventional MRF method utilizes an approximate inverse Fourier transformation for the highly undersampled data in the Fourier domain, leading to aliasing errors in the reconstructed magnetization courses. Computationally expensive statistical MRF modeling approaches overcome this issue by modeling the data directly in the Fourier domain. However, this leads to a non-convex and large-scale optimization task that is challenging to solve and requires expensive calculations. We compare two recent approaches, namely the conventional MRF method and a statistical MRF modeling approach based on Bayesian statistics in terms of their accuracy, reliability and computational costs. The comparison is carried out for simulated data with known ground truth for different signal-to-noise ratios, in the presence of errors in the physical model, and for several Fourier domain sampling schemes. It is demonstrated that a residual analysis can help to decide if the conventional MRF method is sufficient or if the complex Bayesian Fourier domain modeling approach can lead to a significant improvement.