Andreas Kofler

Felix Frederik Zimmermann, Andreas Kofler

We present a novel learned image reconstruction method for accelerated cardiac MRI with multiple receiver coils based on deep convolutional neural networks (CNNs) and algorithm unrolling. In contrast to many existing learned MR image reconstruction techniques that necessitate coil-sensitivity map (CSM) estimation as a distinct network component, our proposed approach avoids explicit CSM estimation. Instead, it implicitly captures and learns to exploit the inter-coil relationships of the images. Our method consists of a series of novel learned image and k-space blocks with shared latent information and adaptation to the acquisition parameters by feature-wise modulation (FiLM), as well as coil-wise data-consistency (DC) blocks. Our method achieved PSNR values of 34.89 and 35.56 and SSIM values of 0.920 and 0.942 in the cine track and mapping track validation leaderboard of the MICCAI STACOM CMRxRecon Challenge, respectively, ranking 4th among different teams at the time of writing. Code will be made available at https://github.com/fzimmermann89/CMRxRecon

Felix F Zimmermann, Christoph Kolbitsch, Patrick Schuenke et al.

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.

Andreas Kofler, Christian Wald, Tobias Schaeffter et al.

Sparsity-based methods have a long history in the field of signal processing and have been successfully applied to various image reconstruction problems. The involved sparsifying transformations or dictionaries are typically either pre-trained using a model which reflects the assumed properties of the signals or adaptively learned during the reconstruction - yielding so-called blind Compressed Sensing approaches. However, by doing so, the transforms are never explicitly trained in conjunction with the physical model which generates the signals. In addition, properly choosing the involved regularization parameters remains a challenging task. Another recently emerged training-paradigm for regularization methods is to use iterative neural networks (INNs) - also known as unrolled networks - which contain the physical model. In this work, we construct an INN which can be used as a supervised and physics-informed online convolutional dictionary learning algorithm. We evaluated the proposed approach by applying it to a realistic large-scale dynamic MR reconstruction problem and compared it to several other recently published works. We show that the proposed INN improves over two conventional model-agnostic training methods and yields competitive results also compared to a deep INN. Further, it does not require to choose the regularization parameters and - in contrast to deep INNs - each network component is entirely interpretable.

Andreas Kofler, Christian Wald, Tobias Schaeffter et al.

The concept of sparsity has been extensively applied for regularization in image reconstruction. Typically, sparsifying transforms are either pre-trained on ground-truth images or adaptively trained during the reconstruction. Thereby, learning algorithms are designed to minimize some target function which encodes the desired properties of the transform. However, this procedure ignores the subsequently employed reconstruction algorithm as well as the physical model which is responsible for the image formation process. Iterative neural networks - which contain the physical model - can overcome these issues. In this work, we demonstrate how convolutional sparsifying filters can be efficiently learned by end-to-end training of iterative neural networks. We evaluated our approach on a non-Cartesian 2D cardiac cine MRI example and show that the obtained filters are better suitable for the corresponding reconstruction algorithm than the ones obtained by decoupled pre-training.

Felix Frederik Zimmermann, Patrick Schuenke, Christoph S. Aigner et al.

We introduce MRpro, an open-source image reconstruction package built upon PyTorch and open data formats. The framework comprises three main areas. First, it provides unified data structures for the consistent manipulation of MR datasets and their associated metadata (e.g., k-space trajectories). Second, it offers a library of composable operators, proximable functionals, and optimization algorithms, including a unified Fourier operator for all common trajectories and an extended phase graph simulation for quantitative MR. These components are used to create ready-to-use implementations of key reconstruction algorithms. Third, for deep learning, MRpro includes essential building blocks such as data consistency layers, differentiable optimization layers, and state-of-the-art backbone networks and integrates public datasets to facilitate reproducibility. MRpro is developed as a collaborative project supported by automated quality control. We demonstrate the versatility of MRpro across multiple applications, including Cartesian, radial, and spiral acquisitions; motion-corrected reconstruction; cardiac MR fingerprinting; learned spatially adaptive regularization weights; model-based learned image reconstruction and quantitative parameter estimation. MRpro offers an extensible framework for MR image reconstruction. With reproducibility and maintainability at its core, it facilitates collaborative development and provides a foundation for future MR imaging research.

Andreas Kofler, Dongyue Si, David Schote et al.

Recent innovations in Magnetic Resonance Imaging (MRI) hardware and software have reignited interest in low-field ($<1\,\mathrm{T}$) and ultra-low-field MRI ($<0.1\,\mathrm{T}$). These technologies offer advantages such as lower power consumption, reduced specific absorption rate, reduced field-inhomogeneities, and cost-effectiveness, presenting a promising alternative for resource-limited and point-of-care settings. However, low-field MRI faces inherent challenges like reduced signal-to-noise ratio and therefore, potentially lower spatial resolution or longer scan times. This chapter examines the challenges and opportunities of low-field and ultra-low-field MRI, with a focus on the role of machine learning (ML) in overcoming these limitations. We provide an overview of deep neural networks and their application in enhancing low-field and ultra-low-field MRI performance. Specific ML-based solutions, including advanced image reconstruction, denoising, and super-resolution algorithms, are discussed. The chapter concludes by exploring how integrating ML with low-field MRI could expand its clinical applications and improve accessibility, potentially revolutionizing its use in diverse healthcare settings.

Thanh Trung Vu, Andreas Kofler, Kostas Papafitsoros

We extend a recently introduced deep unrolling framework for learning spatially varying regularisation parameters in inverse imaging problems to the case of Total Generalised Variation (TGV). The framework combines a deep convolutional neural network (CNN) inferring the two spatially varying TGV parameters with an unrolled algorithmic scheme that solves the corresponding variational problem. The two subnetworks are jointly trained end-to-end in a supervised fashion and as such the CNN learns to compute those parameters that drive the reconstructed images as close to the ground truth as possible. Numerical results in image denoising and MRI reconstruction show a significant qualitative and quantitative improvement compared to the best TGV scalar parameter case as well as to other approaches employing spatially varying parameters computed by unsupervised methods. We also observe that the inferred spatially varying parameter maps have a consistent structure near the image edges, asking for further theoretical investigations. In particular, the parameter that weighs the first-order TGV term has a triple-edge structure with alternating high-low-high values whereas the one that weighs the second-order term attains small values in a large neighbourhood around the edges.

Andreas Kofler, Marc Dewey, Tobias Schaeffter et al.

In this work, we propose an iterative reconstruction scheme (ALONE - Adaptive Learning Of NEtworks) for 2D radial cine MRI based on ground truth-free unsupervised learning of shallow convolutional neural networks. The network is trained to approximate patches of the current estimate of the solution during the reconstruction. By imposing a shallow network topology and constraining the $L_2$-norm of the learned filters, the network's representation power is limited in order not to be able to recover noise. Therefore, the network can be interpreted to perform a low dimensional approximation of the patches for stabilizing the inversion process. We compare the proposed reconstruction scheme to two ground truth-free reconstruction methods, namely a well known Total Variation (TV) minimization and an unsupervised adaptive Dictionary Learning (DIC) method. The proposed method outperforms both methods with respect to all reported quantitative measures. Further, in contrast to DIC, where the sparse approximation of the patches involves the solution of a complex optimization problem, ALONE only requires a forward pass of all patches through the shallow network and therefore significantly accelerates the reconstruction.

Andreas Kofler, Markus Haltmeier, Tobias Schaeffter et al.

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded neural networks have been reported to achieve state-of-the-art results with respect to various quantitative quality measures as PSNR, NRMSE and SSIM across different imaging modalities. However, the fact that these approaches employ the forward and adjoint operators repeatedly in the network architecture requires the network to process the whole images or volumes at once, which for some applications is computationally infeasible. In this work, we follow a different reconstruction strategy by decoupling the regularization of the solution from ensuring consistency with the measured data. The regularization is given in the form of an image prior obtained by the output of a previously trained neural network which is used in a Tikhonov regularization framework. By doing so, more complex and sophisticated network architectures can be used for the removal of the artefacts or noise than it is usually the case in iterative networks. Due to the large scale of the considered problems and the resulting computational complexity of the employed networks, the priors are obtained by processing the images or volumes as patches or slices. We evaluated the method for the cases of 3D cone-beam low dose CT and undersampled 2D radial cine MRI and compared it to a total variation-minimization-based reconstruction algorithm as well as to a method with regularization based on learned overcomplete dictionaries. The proposed method outperformed all the reported methods with respect to all chosen quantitative measures and further accelerates the regularization step in the reconstruction by several orders of magnitude.