Florian Knoll

Kerstin Hammernik, Thomas Küstner, Burhaneddin Yaman et al.

Physics-driven deep learning methods have emerged as a powerful tool for computational magnetic resonance imaging (MRI) problems, pushing reconstruction performance to new limits. This article provides an overview of the recent developments in incorporating physics information into learning-based MRI reconstruction. We consider inverse problems with both linear and non-linear forward models for computational MRI, and review the classical approaches for solving these. We then focus on physics-driven deep learning approaches, covering physics-driven loss functions, plug-and-play methods, generative models, and unrolled networks. We highlight domain-specific challenges such as real- and complex-valued building blocks of neural networks, and translational applications in MRI with linear and non-linear forward models. Finally, we discuss common issues and open challenges, and draw connections to the importance of physics-driven learning when combined with other downstream tasks in the medical imaging pipeline.

Martin Zach, Florian Knoll, Thomas Pock

Data-driven approaches recently achieved remarkable success in magnetic resonance imaging (MRI) reconstruction, but integration into clinical routine remains challenging due to a lack of generalizability and interpretability. In this paper, we address these challenges in a unified framework based on generative image priors. We propose a novel deep neural network based regularizer which is trained in a generative setting on reference magnitude images only. After training, the regularizer encodes higher-level domain statistics which we demonstrate by synthesizing images without data. Embedding the trained model in a classical variational approach yields high-quality reconstructions irrespective of the sub-sampling pattern. In addition, the model shows stable behavior when confronted with out-of-distribution data in the form of contrast variation. Furthermore, a probabilistic interpretation provides a distribution of reconstructions and hence allows uncertainty quantification. To reconstruct parallel MRI, we propose a fast algorithm to jointly estimate the image and the sensitivity maps. The results demonstrate competitive performance, on par with state-of-the-art end-to-end deep learning methods, while preserving the flexibility with respect to sub-sampling patterns and allowing for uncertainty quantification.

Martin Benning, Florian Knoll, Carola-Bibiane Schönlieb et al.

We are presenting a modification of the well-known Alternating Direction Method of Multipliers (ADMM) algorithm with additional preconditioning that aims at solving convex optimisation problems with nonlinear operator constraints. Connections to the recently developed Nonlinear Primal-Dual Hybrid Gradient Method (NL-PDHGM) are presented, and the algorithm is demonstrated to handle the nonlinear inverse problem of parallel Magnetic Resonance Imaging (MRI).

Sheheryar Mehmood, Florian Knoll, Peter Ochs

Algorithm unrolling is ubiquitous in machine learning, particularly in hyperparameter optimization and meta-learning, where Jacobians of solution mappings are computed by differentiating through iterative algorithms. Although unrolling is known to yield asymptotically correct Jacobians under suitable conditions, recent work has shown that the derivative iterates may initially diverge from the true Jacobian, a phenomenon known as the curse of unrolling. In this work, we provide a non-asymptotic analysis that explains the origin of this behavior and identifies the algorithmic factors that govern it. We show that truncating early iterations of the derivative computation mitigates the curse while simultaneously reducing memory requirements. Finally, we demonstrate that warm-starting in bilevel optimization naturally induces an implicit form of truncation, providing a practical remedy. Our theoretical findings are supported by numerical experiments on representative examples.

Marc Vornehm, Chong Chen, Muhammad Ahmad Sultan et al.

Cardiovascular magnetic resonance imaging is a powerful diagnostic tool for assessing cardiac structure and function. However, traditional breath-held imaging protocols pose challenges for patients with arrhythmias or limited breath-holding capacity. This work aims to overcome these limitations by developing a reconstruction framework that enables high-quality imaging in free-breathing conditions for various dynamic cardiac MRI protocols. Multi-Dynamic Deep Image Prior (M-DIP), a novel unsupervised reconstruction framework for accelerated real-time cardiac MRI, is introduced. To capture contrast or content variation, M-DIP first employs a spatial dictionary to synthesize a time-dependent intermediate image. Then, this intermediate image is further refined using time-dependent deformation fields that model cardiac and respiratory motion. Unlike prior DIP-based methods, M-DIP simultaneously captures physiological motion and frame-to-frame content variations, making it applicable to a wide range of dynamic applications. We validate M-DIP using simulated MRXCAT cine phantom data as well as free-breathing real-time cine, single-shot late gadolinium enhancement (LGE), and first-pass perfusion data from clinical patients. Comparative analyses against state-of-the-art supervised and unsupervised approaches demonstrate M-DIP's performance and versatility. M-DIP achieved better image quality metrics on phantom data, higher reader scores on in-vivo cine and LGE data, and comparable scores on in-vivo perfusion data relative to another DIP-based approach. M-DIP enables high-quality reconstructions of real-time free-breathing cardiac MRI without requiring external training data. Its ability to model physiological motion and content variations makes it a promising approach for various dynamic imaging applications.

Jinho Kim, Marcel Dominik Nickel, Florian Knoll

Purpose: To investigate the feasibility of applying zero-shot self-supervised learning reconstruction to reduce breath-hold times in magnetic resonance cholangiopancreatography (MRCP). Methods: Breath-hold MRCP was acquired from 11 healthy volunteers on a 3T scanner using an incoherent k-space sampling pattern leading to a breath-hold duration of 14s. We evaluated zero-shot reconstruction of breath-hold MRCP against parallel imaging of respiratory-triggered MRCP acquired in 338s on average and compressed sensing reconstruction of breath-hold MRCP. To address the long computation times of zero-shot trainings, we used a training approach that leverages a pretrained network to reduce backpropagation depth during training. Results: Zero-shot learning reconstruction significantly improved visual image quality compared to compressed sensing reconstruction, particularly in terms of signal-to-noise ratio and ductal delineation, and reached a level of quality comparable to that of successful respiratory-triggered acquisitions with regular breathing patterns. Shallow training provided nearly equivalent reconstruction performance with a training time of 11 minutes in comparison to 271 minutes for a conventional zero-shot training. Conclusion: Zero-shot learning delivers high-fidelity MRCP reconstructions with reduced breath-hold times, and shallow training offers a practical solution for translation to time-constrained clinical workflows.

Eddy Solomon, Patricia M. Johnson, Zhengguo Tan et al.

This data curation work introduces the first large-scale dataset of radial k-space and DICOM data for breast DCE-MRI acquired in diagnostic breast MRI exams. Our dataset includes case-level labels indicating patient age, menopause status, lesion status (negative, benign, and malignant), and lesion type for each case. The public availability of this dataset and accompanying reconstruction code will support research and development of fast and quantitative breast image reconstruction and machine learning methods.

Jinho Kim, Marcel Dominik Nickel, Florian Knoll

The purpose of this study was to accelerate MR cholangiopancreatography (MRCP) acquisitions using deep learning-based (DL) reconstruction at 3T and 0.55T. A total of 35 healthy volunteers underwent conventional two-fold accelerated MRCP scans at field strengths of 3T and 0.55T. We trained DL reconstructions using two different training strategies, supervised (SV) and self-supervised (SSV), with retrospectively six-fold undersampled data obtained at 3T. We then evaluated the DL reconstructions against standard techniques, parallel imaging (PI) and compressed sensing (CS), focusing on peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as metrics. We also tested DL reconstructions with prospectively accelerated acquisitions and evaluated their robustness when changing fields strengths from 3T to 0.55T. DL reconstructions demonstrated a reduction in average acquisition time from 599/542 to 255/180 seconds for MRCP at 3T/0.55T. In both retrospective and prospective undersampling, PSNR and SSIM of DL reconstructions were higher than those of PI and CS. At the same time, DL reconstructions preserved the image quality of undersampled data, including sharpness and the visibility of hepatobiliary ducts. In addition, both DL approaches produced high-quality reconstructions at 0.55T. In summary, DL reconstructions trained for highly accelerated MRCP enabled a reduction in acquisition time by a factor of 2.4/3.0 at 3T/0.55T while maintaining the image quality of conventional acquisitions.

Marcelo V. W. Zibetti, Florian Knoll, Ravinder R. Regatte

Purpose: To propose an alternating learning approach to learn the sampling pattern (SP) and the parameters of variational networks (VN) in accelerated parallel magnetic resonance imaging (MRI). Methods: The approach alternates between improving the SP, using bias-accelerated subset selection, and improving parameters of the VN, using ADAM with monotonicity verification. The algorithm learns an effective pair: an SP that captures fewer k-space samples generating undersampling artifacts that are removed by the VN reconstruction. The proposed approach was tested for stability and convergence, considering different initial SPs. The quality of the VNs and SPs was compared against other approaches, including joint learning methods and VN learning with fixed variable density Poisson-disc SPs, using two different datasets and different acceleration factors (AF). Results: The root mean squared error (RMSE) improvements ranged from 14.9% to 51.2% considering AF from 2 to 20 in the tested brain and knee joint datasets when compared to the other approaches. The proposed approach has shown stable convergence, obtaining similar SPs with the same RMSE under different initial conditions. Conclusion: The proposed approach was stable and learned effective SPs with the corresponding VN parameters that produce images with better quality than other approaches, improving accelerated parallel MRI applications.

Ruiyang Zhao, Burhaneddin Yaman, Yuxin Zhang et al.

Improving speed and image quality of Magnetic Resonance Imaging (MRI) via novel reconstruction approaches remains one of the highest impact applications for deep learning in medical imaging. The fastMRI dataset, unique in that it contains large volumes of raw MRI data, has enabled significant advances in accelerating MRI using deep learning-based reconstruction methods. While the impact of the fastMRI dataset on the field of medical imaging is unquestioned, the dataset currently lacks clinical expert pathology annotations, critical to addressing clinically relevant reconstruction frameworks and exploring important questions regarding rendering of specific pathology using such novel approaches. This work introduces fastMRI+, which consists of 16154 subspecialist expert bounding box annotations and 13 study-level labels for 22 different pathology categories on the fastMRI knee dataset, and 7570 subspecialist expert bounding box annotations and 643 study-level labels for 30 different pathology categories for the fastMRI brain dataset. The fastMRI+ dataset is open access and aims to support further research and advancement of medical imaging in MRI reconstruction and beyond.

Dominik Narnhofer, Alexander Effland, Erich Kobler et al.

Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less frequently systematically analyzed. In this work, we introduce a Bayesian variational framework to quantify the epistemic uncertainty. To this end, we solve the linear inverse problem of undersampled MRI reconstruction in a variational setting. The associated energy functional is composed of a data fidelity term and the total deep variation (TDV) as a learned parametric regularizer. To estimate the epistemic uncertainty we draw the parameters of the TDV regularizer from a multivariate Gaussian distribution, whose mean and covariance matrix are learned in a stochastic optimal control problem. In several numerical experiments, we demonstrate that our approach yields competitive results for undersampled MRI reconstruction. Moreover, we can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability.

Matthew J. Muckley, Bruno Riemenschneider, Alireza Radmanesh et al.

Accelerating MRI scans is one of the principal outstanding problems in the MRI research community. Towards this goal, we hosted the second fastMRI competition targeted towards reconstructing MR images with subsampled k-space data. We provided participants with data from 7,299 clinical brain scans (de-identified via a HIPAA-compliant procedure by NYU Langone Health), holding back the fully-sampled data from 894 of these scans for challenge evaluation purposes. In contrast to the 2019 challenge, we focused our radiologist evaluations on pathological assessment in brain images. We also debuted a new Transfer track that required participants to submit models evaluated on MRI scanners from outside the training set. We received 19 submissions from eight different groups. Results showed one team scoring best in both SSIM scores and qualitative radiologist evaluations. We also performed analysis on alternative metrics to mitigate the effects of background noise and collected feedback from the participants to inform future challenges. Lastly, we identify common failure modes across the submissions, highlighting areas of need for future research in the MRI reconstruction community.

Oliver Maier, Steven H. Baete, Alexander Fyrdahl et al.

Purpose: The aim of this work is to shed light on the issue of reproducibility in MR image reconstruction in the context of a challenge. Participants had to recreate the results of "Advances in sensitivity encoding with arbitrary k-space trajectories" by Pruessmann et al. Methods: The task of the challenge was to reconstruct radially acquired multi-coil k-space data (brain/heart) following the method in the original paper, reproducing its key figures. Results were compared to consolidated reference implementations created after the challenge, accounting for the two most common programming languages used in the submissions (Matlab/Python). Results: Visually, differences between submissions were small. Pixel-wise differences originated from image orientation, assumed field-of-view or resolution. The reference implementations were in good agreement, both visually and in terms of image similarity metrics. Discussion and Conclusion: While the description level of the published algorithm enabled participants to reproduce CG-SENSE in general, details of the implementation varied, e.g., density compensation or Tikhonov regularization. Implicit assumptions about the data lead to further differences, emphasizing the importance of sufficient meta-data accompanying open data sets. Defining reproducibility quantitatively turned out to be non-trivial for this image reconstruction challenge, in the absence of ground-truth results. Typical similarity measures like NMSE of SSIM were misled by image intensity scaling and outlier pixels. Thus, to facilitate reproducibility, researchers are encouraged to publish code and data alongside the original paper. Future methodological papers on MR image reconstruction might benefit from the consolidated reference implementations of CG-SENSE presented here, as a benchmark for methods comparison.

Anuroop Sriram, Jure Zbontar, Tullie Murrell et al.

The slow acquisition speed of magnetic resonance imaging (MRI) has led to the development of two complementary methods: acquiring multiple views of the anatomy simultaneously (parallel imaging) and acquiring fewer samples than necessary for traditional signal processing methods (compressed sensing). While the combination of these methods has the potential to allow much faster scan times, reconstruction from such undersampled multi-coil data has remained an open problem. In this paper, we present a new approach to this problem that extends previously proposed variational methods by learning fully end-to-end. Our method obtains new state-of-the-art results on the fastMRI dataset for both brain and knee MRIs.

Florian Knoll, Tullie Murrell, Anuroop Sriram et al.

Purpose: To advance research in the field of machine learning for MR image reconstruction with an open challenge. Methods: We provided participants with a dataset of raw k-space data from 1,594 consecutive clinical exams of the knee. The goal of the challenge was to reconstruct images from these data. In order to strike a balance between realistic data and a shallow learning curve for those not already familiar with MR image reconstruction, we ran multiple tracks for multi-coil and single-coil data. We performed a two-stage evaluation based on quantitative image metrics followed by evaluation by a panel of radiologists. The challenge ran from June to December of 2019. Results: We received a total of 33 challenge submissions. All participants chose to submit results from supervised machine learning approaches. Conclusion: The challenge led to new developments in machine learning for image reconstruction, provided insight into the current state of the art in the field, and highlighted remaining hurdles for clinical adoption.

Florian Knoll, Kerstin Hammernik, Chi Zhang et al.

Following the success of deep learning in a wide range of applications, neural network-based machine learning techniques have received interest as a means of accelerating magnetic resonance imaging (MRI). A number of ideas inspired by deep learning techniques from computer vision and image processing have been successfully applied to non-linear image reconstruction in the spirit of compressed sensing for both low dose computed tomography and accelerated MRI. The additional integration of multi-coil information to recover missing k-space lines in the MRI reconstruction process, is still studied less frequently, even though it is the de-facto standard for currently used accelerated MR acquisitions. This manuscript provides an overview of the recent machine learning approaches that have been proposed specifically for improving parallel imaging. A general background introduction to parallel MRI is given that is structured around the classical view of image space and k-space based methods. Both linear and non-linear methods are covered, followed by a discussion of recent efforts to further improve parallel imaging using machine learning, and specifically using artificial neural networks. Image-domain based techniques that introduce improved regularizers are covered as well as k-space based methods, where the focus is on better interpolation strategies using neural networks. Issues and open problems are discussed as well as recent efforts for producing open datasets and benchmarks for the community.

Jure Zbontar, Florian Knoll, Anuroop Sriram et al.

Accelerating Magnetic Resonance Imaging (MRI) by taking fewer measurements has the potential to reduce medical costs, minimize stress to patients and make MRI possible in applications where it is currently prohibitively slow or expensive. We introduce the fastMRI dataset, a large-scale collection of both raw MR measurements and clinical MR images, that can be used for training and evaluation of machine-learning approaches to MR image reconstruction. By introducing standardized evaluation criteria and a freely-accessible dataset, our goal is to help the community make rapid advances in the state of the art for MR image reconstruction. We also provide a self-contained introduction to MRI for machine learning researchers with no medical imaging background.

Kerstin Hammernik, Teresa Klatzer, Erich Kobler et al.

Purpose: To allow fast and high-quality reconstruction of clinical accelerated multi-coil MR data by learning a variational network that combines the mathematical structure of variational models with deep learning. Theory and Methods: Generalized compressed sensing reconstruction formulated as a variational model is embedded in an unrolled gradient descent scheme. All parameters of this formulation, including the prior model defined by filter kernels and activation functions as well as the data term weights, are learned during an offline training procedure. The learned model can then be applied online to previously unseen data. Results: The variational network approach is evaluated on a clinical knee imaging protocol. The variational network reconstructions outperform standard reconstruction algorithms in terms of image quality and residual artifacts for all tested acceleration factors and sampling patterns. Conclusion: Variational network reconstructions preserve the natural appearance of MR images as well as pathologies that were not included in the training data set. Due to its high computational performance, i.e., reconstruction time of 193 ms on a single graphics card, and the omission of parameter tuning once the network is trained, this new approach to image reconstruction can easily be integrated into clinical workflow.