Reconstruction strategy for echo planar spectroscopy and its application to partially undersampled imaging.

The most commonly encountered form of echo planar spectroscopy involves oscillating gradients in one spatial dimension during readout. Data are consequently not sampled on a Cartesian grid. A fast gridding algorithm applicable to this particular situation is presented. The method is optimal, i.e., it performs as well as the full discrete Fourier transform for band limited signals while allowing for use of the fast Fourier transform. The method is demonstrated for reconstruction of data that are partially undersampled in the time domain. The advantages of undersampling are lower hardware requirements or fewer interleaves per acquisition. The method is of particular interest when large bandwidths are needed (e.g., for high field scanning) and for scanners with limited gradient performance. The unavoidable artifacts resulting from undersampling are demonstrated to be acceptable for spectroscopy with long echo times

MR image reconstruction using deep density priors

Algorithms for Magnetic Resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this article, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically Variational Autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers (N=8) and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. Keywords: Reconstruction, MRI, prior probability, machine learning, deep learning, unsupervised learning, density estimationComment: Published in IEEE TMI. Main text and supplementary material, 19 pages tota

2D sense for faster 3D MRI

Sensitivity encoding in two spatial dimensions (2D SENSE) with a receiver coil array is discussed as a means of improving the encoding efficiency of three-dimensional (3D) Fourier MRI. it is shown that in Fourier imaging with two phase encoding directions, 2D SENSE has key advantages over one-dimensional parallel imaging approaches. By exploiting two dimensions for hybrid encoding, the conditioning of the reconstruction problem can be considerably improved, resulting in superior signal-to-noise behavior. As a consequence, 2D SENSE permits greater scan time reduction, which particularly benefits the inherently time-consuming 3D techniques. Along with the principles of 2D SENSE imaging, the properties of the technique are discussed and investigated by means of simulations. Special attention is given to the role of the coil configuration, yielding practical setups with four and six coils. The in vivo feasibility of the two-dimensional approach is demonstrated for 3D head imaging, permitting four-fold scan time reductio

A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction

The acquisition of Magnetic Resonance Imaging (MRI) is inherently slow. Inspired by recent advances in deep learning, we propose a framework for reconstructing MR images from undersampled data using a deep cascade of convolutional neural networks to accelerate the data acquisition process. We show that for Cartesian undersampling of 2D cardiac MR images, the proposed method outperforms the state-of-the-art compressed sensing approaches, such as dictionary learning-based MRI (DLMRI) reconstruction, in terms of reconstruction error, perceptual quality and reconstruction speed for both 3-fold and 6-fold undersampling. Compared to DLMRI, the error produced by the method proposed is approximately twice as small, allowing to preserve anatomical structures more faithfully. Using our method, each image can be reconstructed in 23 ms, which is fast enough to enable real-time applications

Bandwidth, expansion, treewidth, separators, and universality for bounded degree graphs

We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an expanding subgraph of G. Our results imply that if one of these parameters is sublinear in the number of vertices of G then so are all the others. This implies for example that graphs of fixed genus have sublinear bandwidth or, more generally, a corresponding result for graphs with any fixed forbidden minor. As a consequence we establish a simple criterion for universality for such classes of graphs and show for example that for each gamma>0 every n-vertex graph with minimum degree ((3/4)+gamma)n contains a copy of every bounded-degree planar graph on n vertices if n is sufficiently large

Adsorption of Selenium and Strontium on Goethite: EXAFS Study and Surface Complexation Modeling of the Ternary Systems

Knowledge of the geochemical behavior of selenium and strontium is critical for the safe disposal of radioactive wastes. Goethite, as one of the most thermodynamically stable and commonly occurring natural iron oxy-hydroxides, promisingly retains these elements. This work comprehensively studies the adsorption of Se(IV) and Sr(II) on goethite. Starting from electrokinetic measurements, the binary and ternary adsorption systems are investigated and systematically compared via batch experiments, EXAFS analysis, and CD-MUSIC modeling. Se(IV) forms bidentate inner-sphere surface complexes, while Sr(II) is assumed to form outer-sphere complexes at low and intermediate pH and inner-sphere complexes at high pH. Instead of a direct interaction between Se(IV) and Sr(II), our results indicate an electrostatically driven mutual enhancement of adsorption. Adsorption of Sr(II) is promoted by an average factor of 5 within the typical groundwater pH range from 6 to 8 for the concentration range studied here. However, the interaction between Se(IV) and Sr(II) at the surface is two-sided, Se(IV) promotes Sr(II) outer-sphere adsorption, but competes for inner-sphere adsorption sites at high pH. The complexity of surfaces is highlighted by the inability of adsorption models to predict isoelectric points without additional constraints

Travelling-wave nuclear magnetic resonance

Nuclear magnetic resonance (NMR) is one of the most versatile experimental methods in chemistry, physics and biology, providing insight into the structure and dynamics of matter at the molecular scale. Its imaging variant-magnetic resonance imaging (MRI)-is widely used to examine the anatomy, physiology and metabolism of the human body. NMR signal detection is traditionally based on Faraday induction in one or multiple radio-frequency resonators that are brought into close proximity with the sample. Alternative principles involving structured-material flux guides, superconducting quantum interference devices, atomic magnetometers, Hall probes or magnetoresistive elements have been explored. However, a common feature of all NMR implementations until now is that they rely on close coupling between the detector and the object under investigation. Here we show that NMR can also be excited and detected by long-range interaction, relying on travelling radio-frequency waves sent and received by an antenna. One benefit of this approach is more uniform coverage of samples that are larger than the wavelength of the NMR signal-an important current issue in MRI of humans at very high magnetic fields. By allowing a significant distance between the probe and the sample, travelling-wave interaction also introduces new possibilities in the design of NMR experiments and systems

Analysis of nickel concentration profiles around the roots of the hyperaccumulator plant Berkheya coddii using MRI and numerical simulations

Investigations of soil-root interactions are hampered by the difficult experimental accessibility of the rhizosphere. Here we show the potential of Magnetic Resonance Imaging (MRI) as a non-destructive measurement technique in combination with numerical modelling to study the dynamics of the spatial distribution of dissolved nickel (Ni2+) around the roots of the nickel hyperaccumulator plant Berkheya coddii. Special rhizoboxes were used in which a root monolayer had been grown, separated from an adjacent inert glass bead packing by a nylon membrane. After applying a Ni2+ solution of 10mgl−1, the rhizobox was imaged repeatedly using MRI. The obtained temporal sequence of 2-dimensional Ni2+ maps in the vicinity of the roots showed that Ni2+ concentrations increased towards the root plane, revealing an accumulation pattern. Numerical modelling supported the Ni2+ distributions to result from advective water flow towards the root plane, driven by transpiration, and diffusion of Ni2+ tending to eliminate the concentration gradient. With the model, we could study how the accumulation pattern of Ni2+ in the root zone transforms into a depletion pattern depending on transpiration rate, solute uptake rate, and Ni2+ concentration in solutio