One of the most promising solutions for uncertainty quantification in high-dimensional statistics is the debiased LASSO that relies on unconstrained ℓ1-minimization. The initial works focused on real Gaussian designs as a toy model for this problem. However, in medical imaging applications, such as compressive sensing for MRI, the measurement system is represented by a (subsampled) complex Fourier matrix. The purpose of this work is to extend the method to the MRI case in order to construct confidence intervals for each pixel of an MR image. We show that a sufficient amount of data is $n \gtrsim \max \left\{ {{s_0}{{\log }^2}{s_0}\log p,{s_0}{{\log }^2}p} \right\}$.

Voluntary and involuntary patient motion is a major problem for data quality in clinical routine of Magnetic Resonance Imaging (MRI). It has been thoroughly investigated and, yet it still remains unresolved. In quantitative MRI, motion artifacts impair the entire temporal evolution of the magnetization and cause errors in parameter estimation. Here, we present a novel strategy based on residual learning for retrospective motion correction in fast 3D whole-brain multiparametric MRI. We propose a 3D multiscale convolutional neural network (CNN) that learns the non-linear relationship between the motion-affected quantitative parameter maps and the residual error to their motion-free reference. For supervised model training, despite limited data availability, we propose a physics-informed simulation to generate self-contained paired datasets from a priori motion-free data. We evaluate motion-correction performance of the proposed method for the example of 3D Quantitative Transient-state Imaging at 1.5T and 3T. We show the robustness of the motion correction for various motion regimes and demonstrate the generalization capabilities of the residual CNN in terms of real-motion in vivo data of healthy volunteers and clinical patient cases, including pediatric and adult patients with large brain lesions. Our study demonstrates that the proposed motion correction outperforms current state of the art, reliably providing a high, clinically relevant image quality for mild to pronounced patient movements. This has important implications in clinical setups where large amounts of motion affected data must be discarded as they are rendered diagnostically unusable.

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study a deep learning approach to address these shortcomings. Coupled with a dimensionality reduction first layer, the proposed MRF-Net is able to reconstruct quantitative maps by saving more than 60 times in memory and computations required for a DM baseline. Fine-grid manifold enumeration i.e. the MRF dictionary is only used for training the network and not during image reconstruction. We show that the MRF-Net provides a piece-wise affine approximation to the Bloch response manifold projection and that rather than memorizing the dictionary, the network efficiently clusters this manifold and learns a set of hierarchical matched-filters for affine regression of the NMR characteristics in each segment.

Magnetic resonance fingerprinting (MRF) quantifies various properties simultaneously by matching measurements to a dictionary of precomputed signals. We propose to extend the MRF framework by using a database to introduce additional parameters and spatial characteristics to the dictionary. We show that, with an adequate matching technique which includes an update of selected fingerprints in parameter space, it is possible to reconstruct parametric maps, synthesize modalities, and label tissue types at the same time directly from an MRF acquisition. We compare (1) relaxation maps from a spatiotemporal dictionary against a temporal MRF dictionary, (2) synthetic diffusion metrics versus those obtained with a standard diffusion acquisition, and (3) anatomical labels generated from MRF signals to an established segmentation method, demonstrating the potential of using MRF for multiparametric brain mapping. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Numerous scientific fields rely on elaborate but partly suboptimal data processing pipelines. An example is diffusion magnetic resonance imaging (diffusion MRI), a non-invasive microstructure assessment method with a prominent application in neuroimaging. Advanced diffusion models providing accurate microstructural characterization so far have required long acquisition times and thus have been inapplicable for children and adults who are uncooperative, uncomfortable, or unwell. We show that the long scan time requirements are mainly due to disadvantages of classical data processing. We demonstrate how deep learning, a group of algorithms based on recent advances in the field of artificial neural networks, can be applied to reduce diffusion MRI data processing to a single optimized step. This modification allows obtaining scalar measures from advanced models at twelve-fold reduced scan time and detecting abnormalities without using diffusion models. We set a new state of the art by estimating diffusion kurtosis measures from only 12 data points and neurite orientation dispersion and density measures from only 8 data points. This allows unprecedentedly fast and robust protocols facilitating clinical routine and demonstrates how classical data processing can be streamlined by means of deep learning.

Diffusion tensor magnetic resonance imaging (DT-MRI) is a non-invasive imaging technique allowing to estimate the molecular self-diffusion tensors of water within surrounding tissue. Due to the low signal-to-noise ratio of magnetic resonance images, reconstructed tensor images usually require some sort of regularization in a post-processing step. Previous approaches are either suboptimal with respect to the reconstructing or regularization step. This paper presents a Bayesian approach for simultaneous reconstructing and regularization of DT-MR images that allows to resolve the disadvantages of previous approaches. To this end, estimation theoretical concepts are generalized to tensor valued images that are considered as Riemannian manifolds. Doing so allows us to derive a maximum a posterior estimator of the tensor image that considers both the statistical characteristics of the Rician noise occurring in MR images as well as the nonlinear structure of tensor valued images. Experiments on synthetic data as well as real DT-MRI data validate the advantage of considering both statistical as well as geometrical characteristics of DT-MRI.