Andreas Kofler

MRpro is an open‐source framework for MR image reconstruction and quantitative parameter estimation, with particular relevance to low‐field MRI. Built on PyTorch, it supports modern deep‐learning reconstructions and standardized data exchange through ISMRMRD for raw k‐space data and DICOM and NIfTI for reconstructed images and parameter maps. This facilitates integration into existing pipelines and the use of data from different devices. MRpro provides unified data structures for the consistent manipulation of MR datasets and associated metadata, together with a library of composable operators, proximable functionals, and optimization algorithms. The operator library includes a unified Fourier operator for all common trajectories and operators specifically developed for low‐field applications, such as a B‐correction operator. Together, these components underpin ready‐to‐use implementations of key reconstruction algorithms. For deep learning, MRpro includes data‐consistency layers, differentiable optimization layers, state‐of‐the‐art backbone networks, and access to public datasets to facilitate reproducibility. Automated quality control supports collaborative development. We demonstrate MRpro for automatic reconstruction, iterative SENSE, deep‐learning‐based reconstruction, and quantitative parameter estimation. For selected Cartesian and non‐Cartesian tasks, iterative SENSE reconstructions from MRpro differed from those obtained with BART, SigPy, and MRIReco by less than 3% relative RMSE. Further applications use public and simulated datasets and measured low‐field data acquired at 0.3 T, 0.6 T, and 47 mT. MRpro provides a reproducible and maintainable foundation for future MR imaging research.

Objective: Magnetic Resonance Elastography (MRE) is a non-invasive imaging technique for mapping biomechanical properties of in vivo tissue, including shear wave speed (SWS), but involves intrinsically slow data acquisition and an ill-posed wave inversion. Instead of relying on handcrafted image priors, we propose a data-driven approach jointly combining image reconstruction and MRE inversion for robust SWS estimation from undersampled k-space data. Methods: Our physics-informed reconstruction framework comprises two blocks: a model-based neural network (NN)-regularized reconstruction module and a phase-gradient inversion (k-MDEV) calculating SWS from the reconstructed images. Concatenating both blocks yields an end-to-end trainable method to estimate SWS directly from measured k-space data. We evaluated the method on retrospectively highly undersampled brain MRE data and compared it to a total variation (TV) minimization-based approach. We assessed the impact of end-to-end training (qualitative images and SWS maps as targets) versus pre-training (qualitative images as targets) and applied the method also to in vivo data. Results: Our approach significantly reduces NRMSE by 30% compared to TV. End-to-end training improves SWS estimation over separate image reconstruction and SWS calculation. Conclusion: Accurate SWS quantification is possible at acceleration factors up to 19. Our method significantly outperforms TV, highlighting the need for data-driven regularization in this challenging MR problem. Further, our approach successfully generalizes to in vivo data. Significance: We present the first end-to-end trainable MRE reconstruction method for estimating SWS maps directly from k-space. NN-based reconstruction can enable rapid stiffness mapping for dynamic studies, functional imaging, and real-time clinical feedback.

Objective: Cardiac quantitative MRI (qMRI) is a powerful imaging technique for diagnosing pathologies such as diffuse myocardial fibrosis. One main challenge is cardiac motion, which requires synchronization of data acquisition with the heartbeat, leading to long scan times. We present a novel deep learning-based image registration method for cardiac qMRI that enables non-rigid motion correction of data acquired continuously over multiple cardiac cycles, thereby reducing scan times. Methods: Our method is a zero-shot approach that utilizes the physical qMRI signal model for accurate motion estimation. Non-rigid motion of dynamic images is estimated with a U-Net-based architecture. This exploits the intrinsic smoothness of cardiac motion, allowing sharing information between neighboring images. The approach is robust to undersampling artifacts, enabling motion estimation from dynamic images reconstructed from very few k-space data even without advanced image reconstruction methods. Results: We evaluated the method for fast cardiac T1 mapping using a Golden radial sampling scheme on numerical simulations and in-vivo acquisitions. On numerical simulations, our method achieved a 61.64% improvement in T1 accuracy. On in-vivo data, our approach yielded a 45.13% improvement in sharpness of T1 maps, and temporal image alignment of motion-corrected dynamics improved on average by 11.78%. Conclusion: Our method enables accurate non-rigid motion correction of highly undersampled cardiac qMRI data obtained from continuously acquired data. Significance: As our method is individually optimized for each scan without the need for training on large datasets, it can easily be adapted to other cardiac qMRI approaches.

Stress perfusion cardiac magnetic resonance is an important technique for examining and assessing the blood supply of the myocardium. Currently, the majority of clinical perfusion scans are evaluated based on visual assessment by experienced clinicians. This makes the process subjective, and to this end, quantitative methods have been proposed to offer a more user-independent assessment of perfusion. These methods, however, rely on time-consuming deconvolution analysis and are susceptible to data outliers caused by artifacts due to cardiac or respiratory motion. In our work, we introduce a novel deep-learning method that integrates the commonly used Fermi function with a neural network architecture for fast, accurate, and robust myocardial perfusion quantification. This approach employs the Fermi model to ensure that the perfusion maps are consistent with measured data, while also utilizing a prior based on a 3D convolutional neural network to generalize spatio-temporal information across different patient data. Our network is trained within a self-supervised learning framework, which circumvents the need for ground-truth perfusion labels that are challenging to obtain. Furthermore, we extended this training methodology by adopting a technique that ensures estimations are resistant to data outliers, thereby improving robustness against motion artifacts. Our simulation experiments demonstrated an overall improvement in the accuracy and robustness of perfusion parameter estimation, consistently outperforming traditional deconvolution analysis algorithms across varying Signal-to-Noise Ratio scenarios in the presence of data outliers. For the in vivo studies, our method generated robust perfusion estimates that aligned with clinical diagnoses, while being approximately five times faster than conventional algorithms.

Objective: We present a model-based image reconstruction approach based on unrolled neural networks which corrects for image distortion and noise in low-field ( $B_{0} \sim$ 50 mT) MRI. Methods: Utilising knowledge about the underlying physics, a novel network architecture (SH-Net) is introduced which involves the estimation of spherical harmonic coefficients to guarantee a spatially smooth field map estimate. The SH-Net is integrated in an end-to-end trainable model which jointly estimates the $B_{0}$ -field map as well as the image. Experiments were conducted on retrospectively simulated low-field data of human knees. Results: We compare our model to different model-based approaches at distinct noise levels and various $B_{0}$ -field distributions. Our results show that our physics-informed neural network approach outperforms the purely model-based methods by improving the PSNR up to 11.7% and the RMSE up to 86.3%. Conclusion: Our end-to-end trained model-based approach outperforms existing methods in reconstructing image and $B_{0}$ -field maps in the low-field regime. Significance: low-field MRI is becoming increasingly more popular as it enables access to MR in challenging situations such as intensive care units or resource poor areas. Our method allows for fast and accurate image reconstruction in such low-field imaging with $B_{0}$ -inhomogeneity compensation under a wide range of various environmental conditions.

Objective. Task-adapted image reconstruction methods using end-to-end trainable neural networks (NNs) have been proposed to optimize reconstruction for subsequent processing tasks, such as segmentation. However, their training typically requires considerable hardware resources and thus, only relatively simple building blocks, e.g. U-Nets, are typically used, which, albeit powerful, do not integrate model-specific knowledge. Approach. In this work, we extend an end-to-end trainable task-adapted image reconstruction method for a clinically realistic reconstruction and segmentation problem of bone and cartilage in 3D knee MRI by incorporating statistical shape models (SSMs). The SSMs model the prior information and help to regularize the segmentation maps as a final post-processing step. We compare the proposed method to a simultaneous multitask learning approach for image reconstruction and segmentation (MTL) and to a complex SSMs-informed segmentation pipeline (SIS). Main results. Our experiments show that the combination of joint end-to-end training and SSMs to further regularize the segmentation maps obtained by MTL highly improves the results, especially in terms of mean and maximal surface errors. In particular, we achieve the segmentation quality of SIS and, at the same time, a substantial model reduction that yields a five-fold decimation in model parameters and a computational speedup of an order of magnitude. Significance. Remarkably, even for undersampling factors of up to R = 8, the obtained segmentation maps are of comparable quality to those obtained by SIS from ground-truth images.

Quantitative Magnetic Resonance Imaging (qMRI) enables the reproducible measurement of biophysical parameters in tissue. The challenge lies in solving a nonlinear, ill-posed inverse problem to obtain the desired tissue parameter maps from acquired raw data. While various learned and non-learned approaches have been proposed, the existing learned methods fail to fully exploit the prior knowledge about the underlying MR physics, i.e. the signal model and the acquisition model. In this paper, we propose PINQI, a novel qMRI reconstruction method that integrates the knowledge about the signal, acquisition model, and learned regularization into a single end-to-end trainable neural network. Our approach is based on unrolled alternating optimization, utilizing differentiable optimization blocks to solve inner linear and non-linear optimization tasks, as well as convolutional layers for regularization of the intermediate qualitative images and parameter maps. This design enables PINQI to leverage the advantages of both the signal model and learned regularization. We evaluate the performance of our proposed network by comparing it with recently published approaches in the context of highly undersampled $T_{1}$ -mapping, using both a simulated brain dataset, as well as real scanner data acquired from a physical phantom and in-vivo data from healthy volunteers. The results demonstrate the superiority of our proposed solution over existing methods and highlight the effectiveness of our method in real-world scenarios.

We introduce a method for the fast estimation of data-adapted, spatially and temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV) minimization. The proposed approach is inspired by recent developments in algorithm unrolling using deep neural networks (NNs) and relies on two distinct subnetworks. The first subnetwork estimates the regularization parameter-map from the input data. The second subnetwork unrolls [Formula: see text] iterations of an iterative algorithm which approximately solves the corresponding TV-minimization problem incorporating the previously estimated regularization parameter-map. The overall network is then trained end-to-end in a supervised learning fashion using pairs of clean and corrupted data but crucially without the need for access to labels for the optimal regularization parameter-maps. We first prove consistency of the unrolled scheme by showing that the unrolled minimizing energy functional used for the supervised learning [Formula: see text]-converges, as [Formula: see text] tends to infinity, to the corresponding functional that incorporates the exact solution map of the TV-minimization problem. Then, we apply and evaluate the proposed method on a variety of large-scale and dynamic imaging problems with retrospectively simulated measurement data for which the automatic computation of such regularization parameters has been so far challenging using the state-of-the-art methods: a 2D dynamic cardiac magnetic resonance imaging (MRI) reconstruction problem, a quantitative brain MRI reconstruction problem, a low-dose computed tomography problem, and a dynamic image denoising problem. The proposed method consistently improves the TV reconstructions using scalar regularization parameters, and the obtained regularization parameter-maps adapt well to imaging problems and data by leading to the preservation of detailed features. Although the choice of the regularization parameter-maps is data-driven and based on NNs, the subsequent reconstruction algorithm is interpretable since it inherits the properties (e.g., convergence guarantees) of the iterative reconstruction method from which the network is implicitly defined.

Objective: We propose a method for the reconstruction of parameter-maps in Quantitative Magnetic Resonance Imaging (QMRI). Methods: Because different quantitative parameter-maps differ from each other in terms of local features, we propose a method where the employed dictionary learning (DL) and sparse coding (SC) algorithms automatically estimate the optimal dictionary-size and sparsity level separately for each parameter-map. We evaluated the method on a $T_{1}$ -mapping QMRI problem in the brain using the BrainWeb data as well as in-vivo brain images acquired on an ultra-high field 7 T scanner. We compared it to a model-based acceleration for parameter mapping (MAP) approach, other sparsity-based methods using total variation (TV), Wavelets (Wl), and Shearlets (Sh) to a method which uses DL and SC to reconstruct qualitative images, followed by a non-linear (DL+Fit). Results: Our algorithm surpasses MAP, TV, Wl, and Sh in terms of RMSE and PSNR. It yields better or comparable results to DL+Fit by additionally significantly accelerating the reconstruction by a factor of approximately seven. Conclusion: The proposed method outperforms the reported methods of comparison and yields accurate $T_{1}$ -maps. Although presented for $T_{1}$ -mapping in the brain, our method's structure is general and thus most probably also applicable for the the reconstruction of other quantitative parameters in other organs. Significance: From a clinical perspective, the obtained $T_{1}$ -maps could be utilized to differentiate between healthy subjects and patients with Alzheimer's disease. From a technical perspective, the proposed unsupervised method could be employed to obtain ground-truth data for the development of data-driven methods based on supervised learning.