The inverse problem of reconstructing MR images $u$ from Fourier ($k$-) space data $f$ takes the form of the optimization problem:

$$\min \| Au - f \|_2^2 + \lambda \mathcal{R}(u).$$ $A=\mathcal{F}_\Omega C$ is the forward operator that describes the MR encoding process. It consists of a Fourier transform $\mathcal{F}_\Omega$ that maps from image space to Fourier ($k$-) space coefficients at the coordinates $\Omega$ and a diagonal matrix $C$ that contains the sensitivity profiles of the receiver coils of the MR system. $\mathcal{R}$ is a regularizer that separates between true image content and artifacts introduced by an accelerated acquisition. It has been demonstrated that deep learning methods that map the image reconstruction optimization problem onto unrolled neural networks and learn a regularizer from training data [1] achieve state of the art performance in public research challenges [2].

In this work, we will present an update on the performance of learned image reconstruction for a range of clinically relevant applications and discuss the issue of missing-, as well as artificially hallucinated fine-detail image features [3]. We will present results for cardiac, oncological and neuroimaging applications, and will also introduce a novel task-based evaluation for the quality of the reconstructed images using the fastMRI+ dataset [4].

[1] K. Hammernik, T. Klatzer, E. Kobler, M. P. Recht, D. K. Sodickson, T. Pock, F. Knoll. Learning a Variational Network for Reconstruction of Accelerated MRI Data, Magnetic Resonance in Medicine 79: 3055–3071, 2018. https://doi.org/10.1002/mrm.26977

[2] M. J. Muckley, B. Riemenschneider, A. Radmanesh, S. Kim, G. Jeong, J. Ko, Y. Jun, H. Shin, D. Hwang, M. Mostapha, S. Arberet, D. Nickel, Z. Ramzi, P. Ciuciu, J.-L. Starck, J. Teuwen, D. Karkalousos, C. Zhang, A. Sriram, Z. Huang, N. Yakubova, Y. W. Lui, F. Knoll. Results of the 2020 fastMRI Challenge for Machine Learning MR Image Reconstruction, IEEE Transactions on Medical Imaging 40: 2306–2317, 2021. https://doi.org/10.1109/TMI.2021.3075856

[3] A. Radmanesh, M. J. Muckley, T. Murrell, E. Lindsey, A. Sriram, F. Knoll, D. K. Sodickson, Y.W. Lui. Exploring the Acceleration Limits of Deep Learning Variational Network–based Two-dimensional Brain MRI, Radiology: Artificial Intelligence 4, 2022. https://doi.org/10.1148/ryai.210313

[4] R. Zhao, B. Yaman, Y. Zhang, R. Stewart, A. Dixon, F. Knoll, Z. Huang, Y. W. Lui, M. S. Hansen, M. P. Lungren. fastMRI+: Clinical Pathology Annotations for Knee and Brain Fully Sampled Multi-Coil MRI Data, Scientific Data 2022 9: 1–6, 2022. https://doi.org/10.1038/s41597-022-01255-z

An MRI scanner roughly allows measuring the Fourier transform of the image representing a volume at user-specified locations. Finding an optimal sampling pattern and reconstruction algorithm is a longstanding issue. While Shannon and compressed sensing theories dominated the field over the last decade, a recent trend is to optimize the sampling scheme for a specific dataset. Early works investigated algorithms that find the best subset among a set of feasible trajectories. More recently, some works proposed to optimize the positions of the sampling locations continuously [3].

In this talk, we will first show that this optimization problem usually possesses a combinatorial number of spurious minimizers [1]. This effect can however be mitigated by using large datasets of signals and specific preconditioning techniques. Unfortunately, the dataset size, the costly reconstruction processes and the computation of the non-uniform Fourier transform makes the problem computationally challenging. By optimizing the sampling density rather than the points locations, we show that the problem can be solved significantly faster while preserving competitive results [2].

[1] A. Gossard, F. de Gournay, P. Weiss. Spurious minimizers in non uniform Fourier sampling optimization, Inverse Problems 38: 105003, 2022.

[2] A. Gossard, F. de Gournay, P. Weiss. Bayesian Optimization of Sampling Densities in MRI, arXiv: 2209.07170, 2022.

[3] G. Wang, T. Luo, J.-F. Nielsen, D. C Noll, J. A Fessler. B-spline parameterized joint optimization of reconstruction and k-space trajectories (BJORK) for accelerated 2d MRI, IEEE Transactions on Medical Imaging 41: 2318--2330, 2022.

Magnetic Resonance Spin Tomography in Time‐Domain (MR-STAT) is an emerging quantitative magnetic resonance imaging technique which aims at obtaining multi-parametric tissue parameter maps (T1, T2, proton density, etc) from short scans. It describes the relationship between the spatial-domain tissue parameters and the time-domain measured signal by using a comprehensive, volumetric forward model. The MR-STAT reconstruction is cast as a large-scale, ODE constrained, nonlinear inversion problem, which is very challenging in terms of both computing time and memory.

In this presentation, I’ll talk about recent progresses about the acceleration strategies for MR-STAT reconstructions, for example, using a neural network model for the solution of the underlying differential equation model, applying alternating direction method of multipliers (ADMM) etc.

In dynamic cardiac Magnetic Resonance Imaging (MRI), one is interested in the assessment of the cardiac function based on a series of images which show the beating heart. Because the measurements typically take place during a breathhold of the patients, it is desirable to accelerate the scan by undersampling the data which yields an ill-posed inverse problem which requires the use of regularization methods. A prominent and successful example of regularization method is the well-known total variation (TV)-minimization approach which imposes sparsity of the image in its gradient domain. Thereby, the choice of the regularization parameter which balances between the data-fidelity term and the TV-term plays a crucial role. Moreover, having only a scalar regularization parameter which globally dictates the strength of the regularization seems to be sub-optimal for various reasons. Intuitively speaking, the strength of the TV-term should be locally dependent based on the content of the image. However, obtaining entire regularization parameter-maps for dynamic problems can be a challenging task. In this work, we propose a simple yet efficient approach for estimating patient-dependent spatio-temporal regularization parameter-maps for dynamic MRI based on TV-minimization. The overall approach is based on recent developments on algorithm unrolling using deep Neural Networks (NNs). A first NN estimates a spatio-temporal regularization parameter-map from an input image which is then fixed and used to formulate a reconstruction problem which a second network – an unrolled scheme using the primal dual hybrid gradient method – approximately solves. The approach combines NNs with a well-established model-based variational method and yields an entirely interpretable and convergent reconstruction scheme which can be used to improve over TV with merely scalar regularization parameters.