A projection algorithm for gradient waveforms design in Magnetic Resonance Imaging

International audienceCollecting the maximal amount of information in a given scanning time is a major concern in Magnetic Resonance Imaging (MRI) to speed up image acquisition. The hardware constraints (gradient magnitude, slew rate, ...), physical distortions (e.g., off-resonance effects) and sampling theorems (Shannon, compressed sensing) must be taken into account simultaneously, which makes this problem extremely challenging. To date, the main approach to design gradient waveform has consisted of selecting an initial shape (e.g. spiral, radial lines, ...) and then traversing it as fast as possible using optimal control. In this paper, we propose an alternative solution which first consists of defining a desired parameterization of the trajectory and then of optimizing for minimal deviation of the sampling points within gradient constraints. This method has various advantages. First, it better preserves the density of the input curve which is critical in sampling theory. Second, it allows to smooth high curvature areas making the acquisition time shorter in some cases. Third, it can be used both in the Shannon and CS sampling theories. Last, the optimized trajectory is computed as the solution of an efficient iterative algorithm based on convex programming. For piecewise linear trajectories, as compared to optimal control reparameterization, our approach generates a gain in scanning time of 10% in echo planar imaging while improving image quality in terms of signal-to-noise ratio (SNR) by more than 6 dB. We also investigate original trajectories relying on traveling salesman problem solutions. In this context, the sampling patterns obtained using the proposed projection algorithm are shown to provide significantly better reconstructions (more than 6 dB) while lasting the same scanning time

Gradient waveform design for variable density sampling in Magnetic Resonance Imaging

Fast coverage of k-space is a major concern to speed up data acquisition in Magnetic Resonance Imaging (MRI) and limit image distortions due to long echo train durations. The hardware gradient constraints (magnitude, slew rate) must be taken into account to collect a sufficient amount of samples in a minimal amount of time. However, sampling strategies (e.g., Compressed Sensing) and optimal gradient waveform design have been developed separately so far. The major flaw of existing methods is that they do not take the sampling density into account, the latter being central in sampling theory. In particular, methods using optimal control tend to agglutinate samples in high curvature areas. In this paper, we develop an iterative algorithm to project any parameterization of k-space trajectories onto the set of feasible curves that fulfills the gradient constraints. We show that our projection algorithm provides a more efficient alternative than existinf approaches and that it can be a way of reducing acquisition time while maintaining sampling density for piece-wise linear trajectories

Assessment of a Neural Network-Based Subspace MRI Reconstruction Method for Myocardial T1 Mapping Using Inversion-Recovery Radial FLASH

openLa mappatura T1 del miocardio si è affermata come un promettente biomarker per la caratterizzazione non invasiva del muscolo cardiaco nell'ambito della risonanza magnetica cardiovascolare. Questo approccio ha il potenziale di sostituire la biopsia nella diagnosi di diverse condizioni patologiche del miocardio, come la fibrosi, l'accumulo di ferro o amiloidosi. Negli ultimi anni, il deep learning ha suscitato un crescente interesse per la ricostruzione delle immagini, portando a notevoli miglioramenti rispetto alle tecniche che richiedono la predefinizione dei parametri di regolarizzazione da parte dell'operatore, rendendo così il processo parzialmente soggettivo. Il miglioramento è reso possibile grazie alla capacità delle reti neurali di apprendere automaticamente le proprietà presenti nelle immagini del dataset utilizzato per il training. La presente tesi si focalizza sull'analisi di un nuovo metodo di ricostruzione subspaziale delle immagini di risonanza magnetica basato su reti neurali per la mappatura T1 del miocardio, che utilizza una sequenza chiamata single-shot inversion-recovery radial FLASH. È stata impiegata una rete neurale nota come NLINV-Net, la quale trae ispirazione dalla tecnica di ricostruzione delle immagini NLINV. NLINV-Net risolve il problema inverso non lineare per il parallel imaging srotolando l'iteratively regularized Gauss-Newton method e incorporando nel processo termini di regolarizzazione basati su reti neurali. La rete neurale ha appreso le correlazioni esistenti tra i singoli parametri codificati dalla sequenza FLASH in modo auto-supervisionato, ovvero senza richiedere un riferimento esterno. NLINV-Net ha dimostrato di superare NLINV per la precisione dei valori T1, producendo mappe T1 di alta qualità. Le mappe ottenute con NLINV-Net sono paragonabili a quelle ottenute con un altro metodo di riferimento, che combina parallel imaging e compressed sensing utilizzando la regolarizzazione l1-Wavelet nella risoluzione del problema lineare inverso per il parallel imaging. Il vantaggio di NLINV-Net rispetto al suddetto metodo di appoggio è quello di sbarazzarsi della predefinizione dei parametri di regolarizzazione da parte dell'operatore. In questo modo, NLINV-Net fornisce una solida base per la mappatura T1 del miocardio utilizzando la sequenza single-shot inversion-recovery radial FLASH.In cardiovascular MRI, myocardial T1 mapping provides an imaging biomarker for the non-invasive characterization of the myocardial tissue, with the potential to replace invasive biopsy for the diagnosis of several pathological heart muscle conditions such as fibrosis, iron overload, or amyloid infiltration. Over the last few years, deep learning has become increasingly appealing for image reconstruction to improve upon the commonly employed user-dependent regularization terms by automatically learning image properties from the training dataset. This thesis investigates a novel neural network-based subspace MRI reconstruction method for myocardial T1 mapping, which uses a single-shot inversion-recovery radial FLASH sequence. The neural network utilized in this study is NLINV-Net, which draws inspiration from the NLINV image reconstruction technique. NLINV-Net addresses the nonlinear inverse problem for parallel imaging by unrolling the iteratively regularized Gauss-Newton method and incorporating neural network-based regularization terms into the process. It learned in a self-supervised fashion, i.e., without a reference, correlations between the individual parameters encoded with the FLASH sequence, and, consequently, a well-tuned regularization. NLINV-Net outperformed NLINV in terms of T1 precision and generated high-quality T1 maps. The T1 maps computed using NLINV-Net were comparable to the ones obtained using another baseline method, which combines parallel imaging and compressed sensing using the l1-Wavelet regularization when solving the linear inverse problem for parallel imaging. In this case, the advantage of NLINV-Net is that it removes the subjective regularization parameter tuning that comes with the forenamed benchmark method. Thus, it provides an excellent basis for myocardial T1 mapping using a single-shot inversion-recovery radial FLASH sequence

Investigation of Sparsifying Transforms in Compressed Sensing for Magnetic Resonance Imaging with Fasttestcs

The goal of this contribution is to achieve higher reduction factors for faster Magnetic Resonance Imaging (MRI) scans with better Image Quality (IQ) by using Compressed Sensing (CS). This can be accomplished by adopting and understanding better sparsifying transforms for CS in MRI. There is a tremendous number of transforms and optional settings potentially available. Additionally, the amount of research in CS is growing, with possible duplication and difficult practical evaluation and comparison. However, no in-depth analysis of the effectiveness of different redundant sparsifying transforms on MRI images with CS has been undertaken until this work. New theoretical sparsity bounds for the dictionary restricted isometry property constants in CS are presented with mathematical proof. In order to verify the sparsifying transforms in this setting, the experiments focus on several redundant transforms contrasting them with orthogonal transforms. The transforms investigated are Wavelet (WT), Cosine (CT), contourlet, curvelet, k-means singular value decomposition, and Gabor. Several variations of these transforms with corresponding filter options are developed and tested in compression and CS simulations. Translation Invariance (TI) in transforms is found to be a key contributing factor in producing good IQ because any particular translation of the signal will not effect the transform representation. Some transforms tested here are TI and many others are made TI by transforming small overlapping image patches. These transforms are tested by comparing different under-sampling patterns and reduction ratios with varying image types including MRI data. Radial, spiral, and various random patterns are implemented and demonstrate that the TIWT is very robust across all under-sampling patterns. Results of the TIWT simulations show improvements in de-noising and artifact suppression over that of individual orthogonal wavelets and total variation ell-1 minimization in CS simulations. Some of these transforms add considerable time to the CS simulations and prohibit extensive testing of large 3D MRI datasets. Therefore, the FastTestCS software simulation framework is developed and customized for testing images, under-samping patterns and sparsifying transforms. This novel software is offered as a practical, robust, universal framework for evaluating and developing simulations in order to quickly test sparsifying transforms for CS MRI

Joint multi-contrast Variational Network reconstruction (jVN) with application to rapid 2D and 3D imaging

Purpose: To improve the image quality of highly accelerated multi-channel MRI data by learning a joint variational network that reconstructs multiple clinical contrasts jointly. Methods: Data from our multi-contrast acquisition was embedded into the variational network architecture where shared anatomical information is exchanged by mixing the input contrasts. Complementary k-space sampling across imaging contrasts and Bunch-Phase/Wave-Encoding were used for data acquisition to improve the reconstruction at high accelerations. At 3T, our joint variational network approach across T1w, T2w and T2-FLAIR-weighted brain scans was tested for retrospective under-sampling at R=6 (2D) and R=4x4 (3D) acceleration. Prospective acceleration was also performed for 3D data where the combined acquisition time for whole brain coverage at 1 mm isotropic resolution across three contrasts was less than three minutes. Results: Across all test datasets, our joint multi-contrast network better preserved fine anatomical details with reduced image-blurring when compared to the corresponding single-contrast reconstructions. Improvement in image quality was also obtained through complementary k-space sampling and Bunch-Phase/Wave-Encoding where the synergistic combination yielded the overall best performance as evidenced by exemplarily slices and quantitative error metrics. Conclusion: By leveraging shared anatomical structures across the jointly reconstructed scans, our joint multi-contrast approach learnt more efficient regularizers which helped to retain natural image appearance and avoid over-smoothing. When synergistically combined with advanced encoding techniques, the performance was further improved, enabling up to R=16-fold acceleration with good image quality. This should help pave the way to very rapid high-resolution brain exams