Learning the Sampling Pattern for MRI

The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long acquisition times can limit its use. In this work, we consider the problem of learning a sparse sampling pattern that can be used to optimally balance acquisition time versus quality of the reconstructed image. We use a supervised learning approach, making the assumption that our training data is representative enough of new data acquisitions. We demonstrate that this is indeed the case, even if the training data consists of just 7 training pairs of measurements and ground-truth images; with a training set of brain images of size 192 by 192, for instance, one of the learned patterns samples only 35% of k-space, however results in reconstructions with mean SSIM 0.914 on a test set of similar images. The proposed framework is general enough to learn arbitrary sampling patterns, including common patterns such as Cartesian, spiral and radial sampling.

Entropic Comparison of Atomic-Resolution Electron Tomography of Crystals and Amorphous Materials

Electron tomography bears promise for widespread determination of the three-dimensional arrangement of atoms in solids. However, it remains unclear whether methods successful for crystals are optimal for amorphous solids. Here, we explore the relative difficulty encountered in atomic-resolution tomography of crystalline and amorphous nanoparticles. We define an informational entropy to reveal the inherent importance of low-entropy zone-axis projections in the reconstruction of crystals. In turn, we propose considerations for optimal sampling for tomography of ordered and disordered materials.

Fast imaging of laboratory core floods using 3D compressed sensing RARE MRI

Three-dimensional (3D) imaging of the fluid distributions within the rock is essential to enable the unambiguous interpretation of core flooding data. Magnetic resonance imaging (MRI) has been widely used to image fluid saturation in rock cores; however, conventional acquisition strategies are typically too slow to capture the dynamic nature of the displacement processes that are of interest. Using Compressed Sensing (CS), it is possible to reconstruct a near-perfect image from significantly fewer measurements than was previously thought necessary, and this can result in a significant reduction in the image acquisition times. In the present study, a method using the Rapid Acquisition with Relaxation Enhancement (RARE) pulse sequence with CS to provide 3D images of the fluid saturation in rock core samples during laboratory core floods is demonstrated. An objective method using image quality metrics for the determination of the most suitable regularisation functional to be used in the CS reconstructions is reported. It is shown that for the present application, Total Variation outperforms the Haar and Daubechies3 wavelet families in terms of the agreement of their respective CS reconstructions with a fully-sampled reference image. Using the CS-RARE approach, 3D images of the fluid saturation in the rock core have been acquired in 16min. The CS-RARE technique has been applied to image the residual water saturation in the rock during a water-water displacement core flood. With a flow rate corresponding to an interstitial velocity of vi=1.89±0.03ftday(-1), 0.1 pore volumes were injected over the course of each image acquisition, a four-fold reduction when compared to a fully-sampled RARE acquisition. Finally, the 3D CS-RARE technique has been used to image the drainage of dodecane into the water-saturated rock in which the dynamics of the coalescence of discrete clusters of the non-wetting phase are clearly observed. The enhancement in the temporal resolution that has been achieved using the CS-RARE approach enables dynamic transport processes pertinent to laboratory core floods to be investigated in 3D on a time-scale and with a spatial resolution that, until now, has not been possible.

Quantitative mapping of chemical compositions with MRI using compressed sensing

In this work, a magnetic resonance (MR) imaging method for accelerating the acquisition time of two dimensional concentration maps of different chemical species in mixtures by the use of compressed sensing (CS) is presented. Whilst 2D-concentration maps with a high spatial resolution are prohibitively time-consuming to acquire using full k-space sampling techniques, CS enables the reconstruction of quantitative concentration maps from sub-sampled k-space data. First, the method was tested by reconstructing simulated data. Then, the CS algorithm was used to reconstruct concentration maps of binary mixtures of 1,4-dioxane and cyclooctane in different samples with a field-of-view of 22mm and a spatial resolution of 344μm×344μm. Spiral based trajectories were used as sampling schemes. For the data acquisition, eight scans with slightly different trajectories were applied resulting in a total acquisition time of about 8min. In contrast, a conventional chemical shift imaging experiment at the same resolution would require about 17h. To get quantitative results, a careful weighting of the regularisation parameter (via the L-curve approach) or contrast-enhancing Bregman iterations are applied for the reconstruction of the concentration maps. Both approaches yield relative errors of the concentration map of less than 2mol-% without any calibration prior to the measurement. The accuracy of the reconstructed concentration maps deteriorates when the reconstruction model is biased by systematic errors such as large inhomogeneities in the static magnetic field. The presented method is a powerful tool for the fast acquisition of concentration maps that can provide valuable information for the investigation of many phenomena in chemical engineering applications.

Variational Depth From Focus Reconstruction

This paper deals with the problem of reconstructing a depth map from a sequence of differently focused images, also known as depth from focus (DFF) or shape from focus. We propose to state the DFF problem as a variational problem, including a smooth but nonconvex data fidelity term and a convex nonsmooth regularization, which makes the method robust to noise and leads to more realistic depth maps. In addition, we propose to solve the nonconvex minimization problem with a linearized alternating directions method of multipliers, allowing to minimize the energy very efficiently. A numerical comparison to classical methods on simulated as well as on real data is presented.

Reduced-dose and high-speed acquisition strategies for multi-dimensional electron microscopy

Multi-dimensional electron microscopy has recently gained considerable interest thanks to the advent of microscopes with unprecedented analytical and in situ capabilities. These information-rich imaging modes, though, are often subject to long acquisition times and large data generation. In this paper, we explore novel acquisition strategies and reconstruction algorithms to retrieve reliable reconstructions from datasets that are limited in terms of both per image and tilt series angular sampling. We show that inpainting techniques are capable of restoring scanning transmission electron microscopy images in which a very restricted number of pixels are scanned, while compressed sensing tomographic reconstruction is capable of minimising artefacts due to angular subsampling. An example of robust reconstruction from data constituting a dose reduction of 10× is presented, using an organic/inorganic core-shell nanowire as a test sample. The combination of these novel acquisition schemes and image recovery strategies provides new avenues to reduced-dose and high-speed imaging.

Ultrashort echo time (UTE) imaging using gradient pre-equalization and compressed sensing

Ultrashort echo time (UTE) imaging is a well-known technique used in medical MRI, however, the implementation of the sequence remains non-trivial. This paper introduces UTE for non-medical applications and outlines a method for the implementation of UTE to enable accurate slice selection and short acquisition times. Slice selection in UTE requires fast, accurate switching of the gradient and r.f. pulses. Here a gradient "pre-equalization" technique is used to optimize the gradient switching and achieve an effective echo time of 10μs. In order to minimize the echo time, k-space is sampled radially. A compressed sensing approach is used to minimize the total acquisition time. Using the corrections for slice selection and acquisition along with novel image reconstruction techniques, UTE is shown to be a viable method to study samples of cork and rubber with a shorter signal lifetime than can typically be measured. Further, the compressed sensing image reconstruction algorithm is shown to provide accurate images of the samples with as little as 12.5% of the full k-space data set, potentially permitting real time imaging of short T2(*) materials.

Ultrafast magnetic-resonance-imaging velocimetry of liquid-liquid systems: overcoming chemical-shift artifacts using compressed sensing

We present simultaneous measurement of dispersed and continuous phase flow fields for liquid-liquid systems obtained using ultrafast magnetic resonance imaging. Chemical-shift artifacts, which are otherwise highly problematic for this type of measurement, are overcome using a compressed sensing based image reconstruction algorithm that accounts for off-resonant signal components. This scheme is combined with high-temporal-resolution spiral imaging (188 frames per second), which is noted for its robustness to flow. It is demonstrated that both quantitative signal intensity and phase preconditioning are preserved throughout the image reconstruction algorithm. Measurements are acquired of oil droplets of varying viscosity rising through stagnant water. From these data it is apparent that the internal droplet flow fields are heavily influenced by the droplet shape oscillations, and that the accurate modeling of droplet shape is of critical importance in the modeling of droplet-side hydrodynamics. The application of the technique to three-component systems is also demonstrated, as is the measurement of local concentration maps of a mutually soluble species (acetone in polydimethylsiloxane-water).

Phase reconstruction from velocity-encoded MRI measurements--a survey of sparsity-promoting variational approaches

In recent years there has been significant developments in the reconstruction of magnetic resonance velocity images from sub-sampled k-space data. While showing a strong improvement in reconstruction quality compared to classical approaches, the vast number of different methods, and the challenges in setting them up, often leaves the user with the difficult task of choosing the correct approach, or more importantly, not selecting a poor approach. In this paper, we survey variational approaches for the reconstruction of phase-encoded magnetic resonance velocity images from sub-sampled k-space data. We are particularly interested in regularisers that correctly treat both smooth and geometric features of the image. These features are common to velocity imaging, where the flow field will be smooth but interfaces between the fluid and surrounding material will be sharp, but are challenging to represent sparsely. As an example we demonstrate the variational approaches on velocity imaging of water flowing through a packed bed of solid particles. We evaluate Wavelet regularisation against Total Variation and the relatively recent second order Total Generalised Variation regularisation. We combine these regularisation schemes with a contrast enhancement approach called Bregman iteration. We verify for a variety of sampling patterns that Morozov's discrepancy principle provides a good criterion for stopping the iterations. Therefore, given only the noise level, we present a robust guideline for setting up a variational reconstruction scheme for MR velocity imaging.

Somatostatin analogue octreotide and inhibition of tumour growth in metastatic endocrine gastroenteropancreatic tumours

Antiproliferative treatment of patients with metastatic endocrine gastroenteropancreatic tumours (GEP) is based mainly on chemotherapeutic protocols whereby drug toxicity is a major handicap. Octreotide is the first choice in the control of hormone mediated symptoms. From retrospective and a few prospective studies it has been suggested that octreotide exhibits antiproliferative properties. The prospective German Sandostatin multicentre phase II trial investigated the effects of 200 micrograms octreotide thrice daily for one year on tumour growth and endocrine abnormalities in 103 patients. Octreotide treatment was continued in those patients responding to the drug until tumour progression occurred. In 28 of those with tumour progression during 200 micrograms thrice daily octreotide dose was increased to 500 micrograms thrice daily. The study sample consisted of 52 patients with computed tomography confirmed tumour progression and 13 patients with stable disease before octreotide treatment, whereas no preobservation period was available in 38 patients. Nineteen patients (36.5%) with computed tomography confirmed tumour progression experienced stabilisation of tumour growth lasting for at least three months. Median duration of stable disease was 18 months. At month 12, stable disease continued in 12 patients, declined after 24 months to nine patients, and after 36 months to five patients. Tumour regression has not been seen in this or other subgroups. In the subgroup with stable disease before octreotide, stable disease continued in 53.8% of patients over 12 months. Increase of octreotide dose to 500 micrograms thrice daily did not influence progression seen during the lower dose with the exception of one patient in whom tumour progression changed to stable disease. No association of tumour size response and patients' characteristics could be detected. The results suggest that octreotide inhibits tumour growth in patients with metastasised endocrine GEP tumours. The antiproliferative effect is, at least in some patients, longlasting. Currently, octreotide can only be recommended as an antiproliferative drug if patients with clearly progressive disease show stabilisation after treatment for three to six months.

Methodological implications of testing anaerobe susceptibility to cephalosporins (cefazolin, cefamandole, cefoxitin)

By simultaneously performing broth dilution, agar dilution, and agar diffusion tests with Bacteroidaceae and Peptococcaceae, the influence of methodology upon the outcome of susceptibility testing to cefazolin, cefamandole and cefoxitin was studied. With beta-lactamase positive and negative Bacteroidaceae, the results of the broth dilution and agar dilution tests were in good agreement for cefoxitin. However, when tested with cefaxolin and cefamandole, beta-lactamase positive Bacteroides strains had mostly high broth dilution MICs and relatively low agar dilution MICs. The statistical analysis of the relationship between zone size and broth dilution or agar dilution MICs frequently showed lack of stochastic linearity or relatively low correlation coefficients.