Accurate segmentation of dense nanoparticles by partially discrete electron tomography

poly-DART: A discrete algebraic reconstruction technique for polychromatic X-ray CT

The discrete algebraic reconstruction technique (DART) is a tomographic method to reconstruct images from X-ray projections in which prior knowledge on the number of object materials is exploited. In monochromatic X-ray CT (e.g., synchrotron), DART has been shown to lead to high-quality reconstructions, even with a low number of projections or a limited scanning view. However, most X-ray sources are polychromatic, leading to beam hardening effects, which significantly degrade the performance of DART. In this work, we propose a new discrete tomography algorithm, poly-DART, that exploits sparsity in the attenuation values using DART and simultaneously accounts for the polychromatic nature of the X-ray source. The results show that poly-DART leads to a vastly improved segmentation on polychromatic data obtained from Monte Carlo simulations as well as on experimental data, compared to DART.

Quantifying Morphology and Diffusion Properties of Mesoporous Carbon From High-Fidelity 3D Reconstructions

A reliable quantitative analysis in electron tomography, which depends on the segmentation of the three-dimensional reconstruction, is challenging because of constraints during tilt-series acquisition (missing wedge) and reconstruction artifacts introduced by reconstruction algorithms such as the Simultaneous Iterative Reconstruction Technique (SIRT) and Discrete Algebraic Reconstruction Technique (DART). We have carefully evaluated the fidelity of segmented reconstructions analyzing a disordered mesoporous carbon used as support in catalysis. Using experimental scanning transmission electron microscopy (STEM) tomography data as well as realistic phantoms, we have quantitatively analyzed the effect on the morphological description as well as on diffusion properties (based on a random-walk particle-tracking simulation) to understand the role of porosity in catalysis. The morphological description of the pore structure can be obtained reliably both using SIRT and DART reconstructions even in the presence of a limited missing wedge. However, the measured pore volume is sensitive to the threshold settings, which are difficult to define globally for SIRT reconstructions. This leads to noticeable variations of the diffusion coefficients in the case of SIRT reconstructions, whereas DART reconstructions resulted in more reliable data. In addition, the anisotropy of the determined diffusion properties was evaluated, which was significant in the presence of a limited missing wedge for SIRT and strongly reduced for DART.

Partial Discreteness: A Novel Prior for Magnetic Resonance Image Reconstruction

An important factor influencing the quality of magnetic resonance (MR) images is the reconstruction method that is employed, and specifically, the type of prior knowledge that is exploited during reconstruction. In this work, we introduce a new type of prior knowledge, partial discreteness (PD), where a small number of regions in the image are assumed to be homogeneous and can be well represented by a constant magnitude. In particular, we mathematically formalize the partial discreteness property based on a Gaussian Mixture Model (GMM) and derive a partial discreteness image representation that characterizes the salient features of partially discrete images: a constant intensity in homogeneous areas and texture in heterogeneous areas. The partial discreteness representation is then used to construct a novel prior dedicated to the reconstruction of partially discrete MR images. The strength of the proposed prior is demonstrated on various simulated and real k-space data-based experiments with partially discrete images. Results demonstrate that the PD algorithm performs competitively with state-of-the-art reconstruction methods, being flexible and easy to implement.

The benefit of thresholding carbon layers in electron tomographic tilt series by intensity downshifting

When performing electron tomography, tilt series of images are often acquired from samples that contain unwanted carbonaceous material, such as an embedding resin, a thin carbon support film or hydrocarbon contamination. The presence of such layers can introduce artefacts in reconstructions, obscuring features of interest. Here, we illustrate the benefit of preprocessing a high-angle annular dark-field tomographic tilt series by thresholding unwanted low-density materials using a simple intensity downshifting procedure. The resulting tomograms have fewer artefacts and segmentation can be performed more accurately. We present two representative examples taken from studies of catalyst nanoparticles and amyloid plaque core material from the human brain.

Integration of TomoPy and the ASTRA toolbox for advanced processing and reconstruction of tomographic synchrotron data

The processing of tomographic synchrotron data requires advanced and efficient software to be able to produce accurate results in reasonable time. In this paper, the integration of two software toolboxes, TomoPy and the ASTRA toolbox, which, together, provide a powerful framework for processing tomographic data, is presented. The integration combines the advantages of both toolboxes, such as the user-friendliness and CPU-efficient methods of TomoPy and the flexibility and optimized GPU-based reconstruction methods of the ASTRA toolbox. It is shown that both toolboxes can be easily installed and used together, requiring only minor changes to existing TomoPy scripts. Furthermore, it is shown that the efficient GPU-based reconstruction methods of the ASTRA toolbox can significantly decrease the time needed to reconstruct large datasets, and that advanced reconstruction methods can improve reconstruction quality compared with TomoPy's standard reconstruction method.

Quantitative 3D analysis of huge nanoparticle assemblies

Nanoparticle assemblies can be investigated in 3 dimensions using electron tomography. However, it is not straightforward to obtain quantitative information such as the number of particles or their relative position. This becomes particularly difficult when the number of particles increases. We propose a novel approach in which prior information on the shape of the individual particles is exploited. It improves the quality of the reconstruction of these complex assemblies significantly. Moreover, this quantitative Sparse Sphere Reconstruction approach yields directly the number of particles and their position as an output of the reconstruction technique, enabling a detailed 3D analysis of assemblies with as many as 10,000 particles. The approach can also be used to reconstruct objects based on a very limited number of projections, which opens up possibilities to investigate beam sensitive assemblies where previous reconstructions with the available electron tomography techniques failed.

Removing the effects of the "dark matter" in tomography

Electron tomography (ET) using different imaging modes has been progressively consolidating its position as a key tool in materials science. The fidelity of a tomographic reconstruction, or tomogram, is affected by several experimental factors. Most often, an unrealistic cloud of intensity that does not correspond to a real material phase of the specimen ("dark matter") blurs the tomograms and enhances artefacts arising from the missing wedge (MW). Here we show that by simple preprocessing of the background level of any tomographic tilt series, it is possible to minimise the negative effects of that "dark matter". Iterative reconstruction algorithms converge better, leading to tomograms with fewer streaking artefacts from the MW, more contrast, and increased accuracy. The conclusions are valid irrespective of the imaging mode used, and the methodology improves the segmentation and visualisation of tomograms of both crystalline and amorphous materials. We show examples of HAADF STEM and BF TEM tomography.

Super-resolution for computed tomography based on discrete tomography

In computed tomography (CT), partial volume effects impede accurate segmentation of structures that are small with respect to the pixel size. In this paper, it is shown that for objects consisting of a small number of homogeneous materials, the reconstruction resolution can be substantially increased without altering the acquisition process. A super-resolution reconstruction approach is introduced that is based on discrete tomography, in which prior knowledge about the materials in the object is assumed. Discrete tomography has already been used to create reconstructions from a low number of projection angles, but in this paper, it is demonstrated that it can also be applied to increase the reconstruction resolution. Experiments on simulated and real μCT data of bone and foam structures show that the proposed method indeed leads to significantly improved structure segmentation and quantification compared with what can be achieved from conventional reconstructions.

A cylindrical specimen holder for electron cryo-tomography

The use of slab-like flat specimens for electron cryo-tomography restricts the range of viewing angles that can be used. This leads to the "missing wedge" problem, which causes artefacts and anisotropic resolution in reconstructed tomograms. Cylindrical specimens provide a way to eliminate the problem, since they allow imaging from a full range of viewing angles around the tilt axis. Such specimens have been used before for tomography of radiation-insensitive samples at room temperature, but never for frozen-hydrated specimens. Here, we demonstrate the use of thin-walled carbon tubes as specimen holders, allowing the preparation of cylindrical frozen-hydrated samples of ribosomes, liposomes and whole bacterial cells. Images acquired from these cylinders have equal quality at all viewing angles, and the accessible tilt range is restricted only by the physical limits of the microscope. Tomographic reconstructions of these specimens demonstrate that the effects of the missing wedge are substantially reduced, and could be completely eliminated if a full tilt range was used. The overall quality of these tomograms is still lower than that obtained by existing methods, but improvements are likely in future.

Three-dimensional chemical mapping by EFTEM-TomoJ including improvement of SNR by PCA and ART reconstruction of volume by noise suppression

Electron tomography is becoming one of the most used methods for structural analysis at nanometric scale in biological and materials sciences. Combined with chemical mapping, it provides qualitative and semiquantitative information on the distribution of chemical elements on a given sample. Due to the current difficulties in obtaining three-dimensional (3D) maps by energy-filtered transmission electron microscopy (EFTEM), the use of 3D chemical mapping has not been widely adopted by the electron microscopy community. The lack of specialized software further complicates the issue, especially in the case of data with a low signal-to-noise ratio (SNR). Moreover, data interpretation is rendered difficult by the absence of efficient segmentation tools. Thus, specialized software for the computation of 3D maps by EFTEM needs to include optimized methods for image series alignment, algorithms to improve SNR, different background subtraction models, and methods to facilitate map segmentation. Here we present a software package (EFTEM-TomoJ, which can be downloaded from http://u759.curie.fr/fr/download/softwares/EFTEM-TomoJ), specifically dedicated to computation of EFTEM 3D chemical maps including noise filtering by image reconstitution based on multivariate statistical analysis. We also present an algorithm named BgART (for background removing algebraic reconstruction technique) allowing the discrimination between background and signal and improving the reconstructed volume in an iterative way.

Diffraction/scattering computed tomography for three-dimensional characterization of multi-phase crystalline and amorphous materials

The three-dimensional characterization method described herein is based on diffraction and scattering techniques combined with tomography and uses the variation of these signals to reconstruct a two-dimensional/three-dimensional structural image. To emphasize the capability of the method in discriminating between different poorly ordered phases, it is named diffraction/scattering computed tomography (DSCT). This combination not only allows structural imaging but also yields an enhancement of the weak signals coming from minor phases, thereby increasing the sensitivity of structural probes. This article reports the suitability of the method for discrimination of polycrystalline and amorphous phases and for extraction of their selective local patterns with a contrast sensitivity of about 0.1% in weight of minor phases relative to the matrix. The required background in tomography is given and then the selectivity of scattering signal, the efficiency of the method, reconstruction artefacts and limitations are addressed. The approach is illustrated through different examples covering a large range of applications based on recent literature, showing the potential of DSCT in crystallography and materials science, particularly when functional and/or precious samples with sub-micrometre features have to be investigated in a nondestructive way.

Recent advances in the application of electron tomography to materials chemistry

Nowadays, tomography plays a central role in pureand applied science, in medicine, and in many branches of engineering and technology. It entails reconstructing the three-dimensional (3D) structure of an object from a tilt series of two-dimensional (2D) images. Its origin goes back to 1917, when Radon showed mathematically how a series of 2D projection images could be converted to the 3D structural one. Tomographic X-ray and positron scanning for 3D medical imaging, with a resolution of ∼1 mm, is now ubiquitous in major hospitals. Electron tomography, a relatively new chemical tool, with a resolution of ∼1 nm, has been recently adopted by materials chemists as an invaluable aid for the 3D study of the morphologies, spatially-discriminating chemical compositions, and defect properties of nanostructured materials. In this Account, we review the advances that have been made in facilitating the recording of the required series of 2D electron microscopic images and the subsequent process of 3D reconstruction of specimens that are vulnerable, to a greater or lesser degree, to electron beam damage. We describe how high-fidelity 3D tomograms may be obtained from relatively few 2D images by incorporating prior structural knowledge into the reconstruction process. In particular, we highlight the vital role of compressed sensing, a recently developed procedure well-known to information theorists that exploits ideas of image compression and "sparsity" (that the important image information can be captured in a reduced data set). We also touch upon another promising approach, "discrete" tomography, which builds into the reconstruction process a prior assumption that the object can be described in discrete terms, such as the number of constituent materials and their expected densities. Other advances made recently that we outline, such as the availability of aberration-corrected electron microscopes, electron wavelength monochromators, and sophisticated specimen goniometers, have all contributed significantly to the further development of quantitative 3D studies of nanostructured materials, including nanoparticle-heterogeneous catalysts, fuel-cell components, and drug-delivery systems, as well as photovoltaic and plasmonic devices, and are likely to enhance our knowledge of many other facets of materials chemistry, such as organic-inorganic composites, solar-energy devices, bionanotechnology, biomineralization, and energy-storage systems composed of high-permittivity metal oxides.