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Sub-sampling is applied to simulated $T_1$-$D$ NMR signals and its influence on inversion performance is evaluated. For this different levels of sub-sampling were employed ranging from the fully sampled signal down to only less than two percent of the original data points. This was combined with multiple sample schemes including fully random sampling, truncation and a combination of both. To compare the performance of different inversion algorithms, the so-generated sub-sampled signals were inverted using Tikhonov regularization, modified total generalized variation (MTGV) regularization, deep learning and a combination of deep learning and Tikhonov regularization. Further, the influence of the chosen cost function on the relative inversion performance was investigated. Overall, it could be shown that for a vast majority of instances, deep learning clearly outperforms regularization based inversion methods, if the signal is fully or close to fully sampled. However, in the case of significantly sub-sampled signals regularization yields better inversion performance than its deep learning counterpart with MTGV clearly prevailing over Tikhonov. Additionally, fully random sampling could be identified as the best overall sampling scheme independent of the inversion method. Finally, it could also be shown that the choice of cost function does vastly influence the relative rankings of the tested inversion algorithms highlighting the importance of choosing the cost function accordingly to experimental intentions.

The concept of deep learning is employed for the inversion of NMR signals and it is shown that NMR signal inversion can be considered as an image-to-image regression problem, which can be treated with a convolutional neural net. It is further outlined, that inversion through deep learning provides a clear efficiency and usability advantage compared to regularization techniques such as Tikhonov and modified total generalized variation (MTGV), because no hyperparemeter selection prior to reconstruction is necessary. The inversion network is applied to simulated NMR signals and the results compared with Tikhonov- and MTGV-regularization. The comparison shows that inversion via deep learning is significantly faster than the latter regularization methods and also outperforms both regularization techniques in nearly all instances.

The concept of generalized cross-validation (GCV) is applied to modified total generalized variation (MTGV) regularization. Current implementations of the MTGV regularization rely on manual (or semi-manual) hyperparameter optimization, which is both time-consuming and subject to bias. The combination of MTGV-regularization and GCV allows for a straightforward hyperparameter search during regularization. This significantly increases the efficiency of the MTGV-method, because it limits the number of hyperparameters, which have to be tested and, improves the practicality of MTGV regularization as a standard technique for inversion of NMR signals. The combined method is applied to simulated and experimental NMR data and the resulting reconstructed distributions are presented. It is shown that for all data sets studied the proposed combination of MTGV and GCV minimizes the GCV score allowing an optimal hyperparameter choice.

Velocity-encoded MRI is an imaging technique used in different areas to assess flow motion. Some applications include medical imaging such as cardiovascular blood flow studies, and industrial settings in the areas of rheology, pipe flows, and reactor hydrodynamics, where the goal is to characterise dynamic components of some quantity of interest. The problem of estimating velocities from such measurements is a nonlinear dynamic inverse problem. To retrieve time-dependent velocity information, careful mathematical modelling and appropriate regularisation is required. In this work, we propose an optimisation algorithm based on non-convex Bregman iteration to jointly estimate velocity-, magnitude- and segmentation-information for the application of bubbly flow imaging. Furthermore, we demonstrate through numerical experiments on synthetic and real data that the joint model improves velocity, magnitude and segmentation over a classical sequential approach., Comment: 22 pages, 8 figures

All imaging modalities such as computed tomography (CT), emission tomography and magnetic resonance imaging (MRI) require a reconstruction approach to produce an image. A common image processing task for applications that utilise those modalities is image segmentation, typically performed posterior to the reconstruction. We explore a new approach that combines reconstruction and segmentation in a unified framework. We derive a variational model that consists of a total variation regularised reconstruction from undersampled measurements and a Chan-Vese based segmentation. We extend the variational regularisation scheme to a Bregman iteration framework to improve the reconstruction and therefore the segmentation. We develop a novel alternating minimisation scheme that solves the non-convex optimisation problem with provable convergence guarantees. Our results for synthetic and real data show that both reconstruction and segmentation are improved compared to the classical sequential approach.

Nuclear magnetic resonance (NMR) spectroscopy exploits the magnetic properties of atomic nuclei to discover the structure, reaction state and chemical environment of molecules. We propose a probabilistic generative model and inference procedures for NMR spectroscopy. Specifically, we use a weighted sum of trigonometric functions undergoing exponential decay to model free induction decay (FID) signals. We discuss the challenges in estimating the components of this general model -- amplitudes, phase shifts, frequencies, decay rates, and noise variances -- and offer practical solutions. We compare with conventional Fourier transform spectroscopy for estimating the relative concentrations of chemicals in a mixture, using synthetic and experimentally acquired FID signals. We find the proposed model is particularly robust to low signal to noise ratios (SNR), and overlapping peaks in the Fourier transform of the FID, enabling accurate predictions (e.g., 1% sensitivity at low SNR) which are not possible with conventional spectroscopy (5% sensitivity)., Comment: 26 pages, 13 figures, 1 table. Submitted for publication

In aquatic plants such as the Characean algae, the force generation that drives cyclosis is localized within the cytoplasm, yet produces fluid flows throughout the vacuole. For this to occur the tonoplast must transmit hydrodynamic shear efficiently. Here, using magnetic resonance velocimetry, we present the first whole-cell measurements of the cross-sectional longitudinal velocity field in Chara corallina and show that it is in quantitative agreement with a recent theoretical analysis of rotational cytoplasmic streaming driven by bidirectional helical forcing in the cytoplasm, with direct shear transmission by the tonoplast., Comment: 5 pages, 3 figures

The unique ability of magnetic resonance imaging (MRI) to provide spatial and temporal information from optically opaque systems, in three dimensions, make it an ideal tool to study the internal motion of rapid granular flows. This paper will focus on the use of ultra-fast velocity compensated MRI measurements to study particle velocity and density distributions in a granular gas, produced by vibrating vertically a bed of mustard seeds at 40 Hz. Specifically, a velocity compensated, double spin-echo, triggered, one-dimensional MRI profiling pulse sequence was developed. This gives an MRI temporal resolution of approximately 2 ms and also minimises MRI velocity artefacts. 12 phase measurements per vibration cycle were used. The data can be used to extract values of the mustard seed average velocity and velocity propagators (probability distributions functions) as a function of the phase of the vibration cycle and vertical height within the cell. The data show strong transient effects during the impact phase of the vibration. A detailed discussion of the temporal passage of the individual phase resolved, height resolved velocity distributions, along with seed velocity propagators at a fix height from the vibrating base is presented.

The dynamics of granular materials, mostly radial and axial segregation in horizontal rotating cylinders filled with millet and poppy seeds, is studied by Magnetic Resonance Imaging (MRI). For the first time, full 3D structures and real-time 2D MRI movies showing the progress of segregation over many hours are reported. Data are acquired with sufficiently high temporal and in-plane spatial resolutions (74 ms and 0.94 mm \times 0.94 mm, respectively), giving new insights into the underlying mechanisms. The millet and poppy mixture composition is calibrated based on the signal intensity and is quantified throughout segregation. As for radial segregation, millet and poppy mixture core formation is observed in cylinders of 75% and 82% filling level. The size of the core is calculated and the avalanche layer thickness is therefore determined. 2D MRI movies showing real-time radial segregation suggests that initial radial segregation is due to the stopping and percolation of poppy seeds. Axial segregation is characterized by the formation, traveling and merging of poppy-rich bands. In all cases studied, the formation of poppy-rich bands is observed, after which individual bands start to travel at \sim 3 \mu m s^{-1} until they are within \sim 3 cm of a stationary band. Adjacent bands then merge into a single, enlarged poppy band as millet seeds move out of the merging region. In both radial and axial segregation, core diffusion is shown to be another mechanism pathway for segregation besides the free surface., Comment: 13 pages, 17 figures