Chirality in inorganic nanoparticles and nanostructures has gained increasing scientific interest, because of the possibility to tune their ability to interact differently with left- and right-handed circularly polarized light. In some cases, the optical activity is hypothesized to originate from a chiral morphology of the nanomaterial. However, quantifying the degree of chirality in objects with sizes of tens of nanometers is far from straightforward. Electron tomography offers the possibility to faithfully retrieve the three-dimensional morphology of nanomaterials, but only a qualitative interpretation of the morphology of chiral nanoparticles has been possible so far. We introduce herein a methodology that enables us to quantify the helicity of complex chiral nanomaterials, based on the geometrical properties of a helix. We demonstrate that an analysis at the single particle level can provide significant insights into the origin of chiroptical properties.

Abstract-Seismic full-waveform inversion tries to estimate subsurface medium parameters from seismic data. Areas with subsurface salt bodies are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath. Accurate reconstruction of their geometry is a challenge for current techniques. This paper presents a parametric level-set method for the reconstruction of salt-bodies in seismic fullwaveform inversion. We split the subsurface model in two parts: a background velocity model and the salt body with known velocity but undetermined shape. The salt geometry is represented by a level-set function that evolves during the inversion. We choose radial basis functions to represent the level-set function, leading to an optimization problem with a modest number of parameters. A common problem with level-set methods is to fine tune the width of the level-set boundary for optimal sensitivity. We propose a robust algorithm that dynamically adapts the width of the levelset boundary to ensure faster convergence. Tests on a suite of idealized salt geometries show that the proposed method is stable against a modest amount of noise. We also extend the method to joint inversion of both the background velocity model and the salt-geometry.

SUMMARYIn seismic exploration, the delineation of large bodies with hard exterior contrasts but nearly constant interior properties is a challenge. Examples include salt diapirs, salt slabs, anhydrite or basalt layers. Salt geometries are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath. This papers introduces a parametric level-set method for the reconstruction of such geometries in seismic full-waveform inversion (FWI). The level-set determines the outline of the salt geometry and evolves during the inversion in terms of its underlying parameters. For the latter, we employ Gaussian radial basis functions that can represent a large class of shapes with a small number of parameters. This keeps the dimensionality of the inverse problem small, which makes it easier to solve. First tests on a simple 2-D square box model show dramatic improvements over classic FWI.

This paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We represent the geometry of the anomaly using a level-set function, which we represent using radial basis functions. We pose the reconstruction problem as a bi-level optimization problem in terms of the background and coefficients for the level-set function. To constrain the background reconstruction we impose smoothness through Tikhonov regularization. The bi-level optimization problem is solved in an alternating fashion; in each iteration we first reconstruct the background and consequently update the level-set function. We test our method on numerical phantoms and show that we can successfully reconstruct the geometry of the anomaly, even from limited data. On these phantoms, our method outperforms Total Variation reconstruction, DART and P-DART.

3D characterization of assemblies of nanoparticles is of great importance to determine their structure–property connection. Such investigations become increasingly more challenging when the assemblies become larger and more compact. In this paper, we propose an optimized approach for electron tomography to minimize artifacts related to beam broadening in high angle annular dark-field scanning transmission electron microscopy mode. These artifacts are typically present at one side of the reconstructed 3D data set for thick nanoparticle assemblies. To overcome this problem, we propose a procedure in which two tomographic tilt series of the same sample are acquired. After acquiring the first series, the sample is flipped over 180°, and a second tilt series is acquired. By merging the two reconstructions, blurring in the reconstructed volume is minimized. Next, this approach is combined with an advanced three-dimensional reconstruction algorithm yielding quantitative structural information. Here, the approach is applied to a thick and compact assembly of spherical Au nanoparticles, but the methodology can we used to investigate a broad range of samples.

Electron tomography is a widely used technique for 3D structural analysis of nanomaterials, but it can cause damage to samples due to high electron doses and long exposure times. To...

SUMMARYFull-waveform inversion attempts to estimate a high-resolution model of the Earth by inverting all the seismic data. This procedure fails if the Earth model contains high-contrast bodies such as salt and if su ciently low frequencies are absent from the data. Salt bodies are important for hydrocarbon exploration because oil or gas reservoirs are often located on their sides or underneath. We represent the shape of the salt body with a level set, constructed from radial basis functions to keep its dimensionality low. We have shown earlier that the salt body can be completely recovered if the sediment structure is already known. In this paper, we propose a strategy to simultaneously reconstruct the sediment and the salt. The sediment is implicitly represented by a bilinear interpolation kernel with a small number of variables. An alternating minimization technique solves the resulting optimization problem. The results on a synthetic model using Gauss-Newton approximation of the Hessian shows the feasibility of the approach.

Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a constrained least-squares problem. As the constraints are non-convex, many approaches for solving it rely on either relaxing the constraints or heuristics. In this paper we propose a novel convex formulation, based on the Lagrange dual of the constrained least-squares problem. The resulting problem is a generalized LASSO problem which can be solved efficiently. It is a relaxation in the sense that it can only be guaranteed to give a feasible solution; not necessarily the optimal one. In exhaustive experiments on small images (2×2, 3 × 3, 4 × 4) we find, however, that if the problem has a unique solution, our dual approach finds it. In case of multiple solutions, our approach finds the commonalities between the solutions. Further experiments on realistic numerical phantoms and an experiment on X-ray dataset show that our method compares favourably to Total Variation and DART.