Deep Learning has become a very promising avenue for magnetic resonance image (MRI) reconstruction. In this work, we explore the potential of unrolled networks for non-Cartesian acquisition settings. We design the NC-PDNet (Non-Cartesian Primal Dual Netwok), the first density-compensated (DCp) unrolled neural network, and validate the need for its key components via an ablation study. Moreover, we conduct some generalizability experiments to test this network in out-of-distribution settings, for example training on knee data and validating on brain data. The results show that NC-PDNet outperforms baseline (U-Net, Deep image prior) models both visually and quantitatively in all settings. In particular, in the 2D multi-coil acquisition scenario, the NC-PDNet provides up to a 1.2dB improvement in peak signal-to-noise ratio (PSNR) over baseline networks, while also allowing a gain of at least 1dB in PSNR in generalization settings. We provide the open-source implementation of NC-PDNet, and in particular the Non-uniform Fourier Transform in TensorFlow, tested on 2D multi-coil and 3D single-coil k-space data.

The Spreading Projection Algorithm for Rapid K-space sampLING, or SPARKLING, is an optimization-driven method that has been recently introduced for accelerated 2D MRI using compressed sensing. It has then been extended to address 3D imaging using either stacks of 2D sampling patterns or a local 3D strategy that optimizes a single sampling trajectory at a time. 2D SPARKLING actually performs variable density sampling (VDS) along a prescribed target density while maximizing sampling efficiency and meeting the gradient-based hardware constraints. However, 3D SPARKLING has remained limited in terms of acceleration factors along the third dimension if one wants to preserve a peaky point spread function (PSF) and thus good image quality. In this paper, in order to achieve higher acceleration factors in 3D imaging while preserving image quality, we propose a new efficient algorithm that performs optimization on full 3D SPARKLING. The proposed implementation based on fast multipole methods (FMM) allows us to design sampling patterns with up to ${10}^{{7}}$ k-space samples, thus opening the door to 3D VDS. We compare multi-CPU and GPU implementations and demonstrate that the latter is optimal for 3D imaging in the high-resolution acquisition regime ( $600\mu $ m isotropic). Finally, we show that this novel optimization for full 3D SPARKLING outperforms stacking strategies or 3D twisted projection imaging through retrospective and prospective studies on NIST phantom and in vivo brain scans at 3 Tesla taking the particular case of ${T}_{{2}}$ *-w imaging. Overall the proposed method allows for 2.5-3.75x shorter scan times compared to GRAPPA-4 parallel imaging acquisition at 3 Tesla without compromising image quality.

Compressed sensing in magnetic resonance imaging essentially involves the optimization of (1) the sampling pattern in k-space under MR hardware constraints and (2) image reconstruction from undersampled k-space data. Recently, deep learning methods have allowed the community to address both problems simultaneously, especially in the non-Cartesian acquisition setting. This work aims to contribute to this field by tackling some major concerns in existing approaches. Particularly, current state-of-the-art learning methods seek hardware compliant k-space sampling trajectories by enforcing the hardware constraints through additional penalty terms in the training loss. Through ablation studies, we rather show the benefit of using a projection step to enforce these constraints and demonstrate that the resulting k-space trajectories are more flexible under a projection-based scheme, which results in superior performance in reconstructed image quality. In 2D studies, our novel method trajectories present an improved image reconstruction quality at a 20-fold acceleration factor on the fastMRI data set with SSIM scores of nearly 0.92–0.95 in our retrospective studies as compared to the corresponding Cartesian reference and also see a 3–4 dB gain in PSNR as compared to earlier state-of-the-art methods. Finally, we extend the algorithm to 3D and by comparing optimization as learning-based projection schemes, we show that data-driven joint learning-based method trajectories outperform model-based methods such as SPARKLING through a 2 dB gain in PSNR and 0.02 gain in SSIM.

Over the last decade, the combination of compressed sensing (CS) with acquisition over multiple receiver coils in magnetic resonance imaging (MRI) has allowed the emergence of faster scans while maintaining a good signal-to-noise ratio (SNR). Self-calibrating techniques, such as ESPiRIT, have become the standard approach to estimating the coil sensitivity maps prior to the reconstruction stage. In this work, we proceed differently and introduce a new calibration-less multi-coil CS reconstruction method. Calibration-less techniques no longer require the prior extraction of sensitivity maps to perform multi-coil image reconstruction but usually alternate estimation sensitivity map estimation and image reconstruction. Here, to get rid of the nonconvexity of the latter approach we reconstruct as many MR images as the number of coils. To compensate for the ill-posedness of this inverse problem, we leverage structured sparsity of the multi-coil images in a wavelet transform domain while adapting to variations in SNR across coils owing to the OSCAR (octagonal shrinkage and clustering algorithm for regression) regularization. Coil-specific complex-valued MR images are thus obtained by minimizing a convex but nonsmooth objective function using the proximal primal-dual Condat-Vù algorithm. Comparison and validation on retrospective Cartesian and non-Cartesian studies based on the Brain fastMRI data set demonstrate that the proposed reconstruction method outperforms the state-of-the-art (${\ell }_1$-ESPIRiT, calibration-less AC-LORAKS and CaLM methods) significantly on magnitude images for the T1 and FLAIR contrasts. Additionally, further validation operated on 8 to 20-fold prospectively accelerated high-resolution ex vivo human brain MRI data collected at 7 Tesla confirms the retrospective results. Overall, OSCAR-based regularization preserves phase information more accurately (both visually and quantitatively) compared to other approaches, an asset that can only be assessed on real prospective experiments.

Purpose: Non‐Cartesian MRI with long arbitrary readout directions are susceptible to off‐resonance artifacts due to patient induced inhomogeneities. This results in degraded image quality with strong signal losses and blurring. Current solutions to address this issue involve correcting the off‐resonance artifacts during image reconstruction or reducing inhomogeneities through improved shimming.Theory: The recently developed SPARKLING algorithm is extended to drastically diminish off‐resonance artifacts by generating temporally smooth k‐space sampling patterns. For doing so, the cost function which is optimized in SPARKLING is modified using a temporal weighting factor. Additionally, oversampling of the center of k‐space beyond the Nyquist criteria is prevented through the use of gridded sampling in the region, enforced with affine constraints.Methods: Prospective k‐space data was acquired at 3 T on new trajectories, and we show robustness to inhomogeneities through in silico experiments by adding through artificial degradation of system shimming. Later on, in vivo experiments were carried out to optimize parameters of the new improvements and benchmark the gain in performance.Results: The improved trajectories allowed for the recovery of signal dropouts observed on original SPARKLING acquisitions at larger field inhomogeneities. Furthermore, imposing gridded sampling at the center of k‐space provided improved reconstructed image quality with limited artifacts.Conclusion: These advancements allowed us for nearly shorter scan time compared to GRAPPA‐p4x1, allowing us to reach 600 µm isotropic resolution in 3D ‐w imaging in just 3.3 min at 3 T with negligible degradation in image quality.

Conception et apprentissage de trajectoires d'échantillonnage non cartésiennes dans l'espace k pour l'IRM 3D accélérée: L'imagerie par résonance magnétique (IRM) est une technique d'imagerie médicale non invasive très répandue qui permet de comprendre les structures des tissus du corps humain. Cependant, sa portée et son utilisation sont fortement limitées par les longs temps d'acquisition, car l'acquisition des données est segmentée en temps et réalisée dans le domaine de Fourier de l'image ou espace k. Les théories d'échantillonnage compressif ont permis d'accéder à des temps d'examen plus courts en collectant moins d'information compressible, en particulier en adoptant d’un échantillonnage à densité variable (EDV) dans l'espace k : les basses fréquences (au centre de l'espace k) doivent être échantillonnées plus densément que les hautes fréquences situées à la périphérie de celui-ci. Un moyen efficace d'obtenir un tel EDV est d'utiliser un échantillonnage non cartésien, où l'espace k est échantillonneur le long de courbes plutôt que de lignes alignées sur une grille cartésienne. Essentiellement, cela implique l'optimisation 1) du modèle d'échantillonnage dans l'espace k sous les contraintes matérielles de l'IRM et 2) la reconstruction de l'image à partir des données sous-échantillonnées de l'espace k. Dans cette thèse, nous abordons les questions ci-dessus dans le contexte de l'IRM 3D accélérée. Tout d'abord, nous étendons l'algorithme SPARKLING développé précédemment à l'imagerie 3D, ce qui permet d'obtenir des trajectoires non cartésiennes conformes aux contraintes matérielles et fidèles à une densité d'échantillonnage cible (DEC) spécifiée par l'utilisateur dans l'espace k. Ensuite, nous abordons le problème des artefacts hors résonance présents au sein des trajectoires SPARKLING en modifiant l'algorithme sous-jacent, afin de permettre la récupération du signal dans les régions où la hors résonance est élevée. Dans la dernière partie de la thèse, nous passons à une approche basée sur l'apprentissage piloté par les données pour apprendre la DEC pour les trajectoires SPARKLING. Enfin, nous proposons une nouvelle approche basée sur l'apprentissage profond pour apprendre des courbes d'échantillonnage de l'espace k conformes aux contraintes matérielles conjointement avec un réseau de reconstruction d'images adapté. Dans l'ensemble, nos efforts dans cette thèse ont permis d'accélérer jusqu'à 20 fois les scans IRM 3D avec une réduction significative des artefacts hors résonance, permettant ainsi une dégradation minimale de la qualité des images reconstruites.