Search results for "X-RAY TOMOGRAPHY"

X-ray Tomography of One-forms with Partial Data

2021

If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.

Tensor tomography in periodic slabs

2017

The X-ray transform on the periodic slab $[0,1]\times\mathbb T^n$, $n\geq0$, has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For tensor fields gauge freedom increases the kernel further, and the X-ray transform is not solenoidally injective unless $n=0$. We characterize the kernel of the geodesic X-ray transform for $L^2$-regular $m$-tensors for any $m\geq0$. The characterization extends to more general manifolds, twisted slabs, including the M\"obius strip as the simplest example.

Pestov identities and X-ray tomography on manifolds of low regularity

2021

We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds $(M,g)$ with $g \in C^{1,1}$. In addition to a proof, we produce a redefinition of simplicity that is compatible with rough geometry. This $C^{1,1}$-regularity is optimal on the H\"older scale. The bulk of the article is devoted to setting up a calculus of differential and curvature operators on the unit sphere bundle atop this non-smooth structure.

Torus computed tomography

2020

We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions, solve a minimization problem associated to Tikhonov regularization in Sobolev spaces and prove that the solution operator provides an admissible regularization strategy with a quantitative stability estimate. This regularization is a simple post-processing low-pass filter for the Fourier series of a phantom. We also study the adjoint and the normal operator of the X-ray transform on the flat torus. The X-ray transform is unitary on the flat torus. We have i…

Sicilian Byzantine Icons through the Use of Non-Invasive Imaging Techniques and Optical Spectroscopy: The Case of the Madonna dell’Elemosina

2021

The iconographic heritage is one of the treasures of Byzantine art that have enriched the south of Italy, and Sicily in particular, since the early 16th century. In this work, the investigations of a Sicilian Icon of Greek-Byzantine origin, the Madonna dell’Elemosina, is reported for the first time. The study was carried out using mainly non-invasive imaging techniques (photography in reflectance and grazing visible light, UV fluorescence, infrared reflectography, radiography, and computed tomography) and spectroscopic techniques (X-ray fluorescence and infrared spectroscopy). The identification of the constituent materials provides a decisive contribution to the correct historical and arti…

How and why does willow biochar increase a clay soil water retention capacity?

2018

Addition of biochar into a soil changes its water retention properties by modifying soil textural and structural properties. In addition, internal micrometer-scale porosity that is able to directly store readily plant available water affects soil water retention properties. This study shows how precise knowledge of the internal micrometer-scale pore size distribution of biochar can deepen the understanding of the biochar-water interactions in soils. The micrometer-scale porosity of willow biochar was quantitatively and qualitatively characterized using X-ray tomography, 3D image analysis and Helium ion microscopy. The effect of biochar application on clay soil water retention was studied by…

Aqueous foam as the carrier phase in the deposition of fibre networks

2015

The effect of steric hindrance on the packing of elongated objects

2016

Fibres of various materials can be deposited to form planar mats of fibres. These kinds of structures have gained substantial attention owing to their direct relation to both large industrial fields, such as paper and nonwovens, and biological structures, such as natural networks of fibrin, actin and collagen. In addition, similar structures are important in new emerging fields such as flexible electronics and tissue engineering. The physical properties of these structures are directly related to the connectivity of the network, thus a thorough understanding of the contact formation of the system is of great importance from both a scientific viewpoint as well as for its application in the e…

3D virtual histopathology of cardiac tissue from Covid-19 patients based on phase-contrast X-ray tomography

2021

eLife 10, e71359 (2021). doi:10.7554/eLife.71359

Tracer migration in crystalline rock : application to geological barriers of nuclear waste storage

2016

This work deals with transport of radionuclides in the geosphere. The subject is investigated through characterisation of water conducting fractures, determining of rock transport properties and development of new methods for characterising geological samples. Here, as is often the case, radionuclide transport is investigated indirectly by characterising the structures, where the transport takes place, and directly by measuring transport properties in the gas phase. First water conducting fractures of three different types and the rock matrix surrounding them were analysed through rock samples from Olkiluoto. The analysis was done using X-ray tomography, the 14C-PMMA autoradiography techniq…