Analysis of Tomographic Reconstruction of 2D Images using the Distribution of Unknown Projection Angles

It is well known that a band-limited signal can be reconstructed from its uniformly spaced samples if the sampling rate is sufficiently high. More recently, it has been proved that one can reconstruct a 1D band-limited signal even if the exact sample locations are unknown, but given just the distribution of the sample locations and their ordering in 1D. In this work, we extend the analytical bounds on the reconstruction error in such scenarios for quasi-bandlimited signals. We also prove that the method for such a reconstruction is resilient to a certain proportion of errors in the specification of the sample location ordering. We then express the problem of tomographic reconstruction of 2D images from 1D Radon projections under unknown angles with known angle distribution, as a special case for reconstruction of quasi-bandlimited signals from samples at unknown locations with known distribution. Building upon our theoretical background, we present asymptotic bounds for 2D quasi-bandlimited image reconstruction from 1D Radon projections in the unknown angles setting, which commonly occurs in cryo-electron microscopy (cryo-EM). To the best of our knowledge, this is the first piece of work to perform such an analysis for 2D cryo-EM, even though the associated reconstruction algorithms have been known for a long time

A subspace-based resolution-enhancing image reconstruction method for few-view differential phase-contrast tomography

It is well known that properly designed image reconstruction methods can facilitate reductions in imaging doses and data-acquisition times in tomographic imaging. The ability to do so is particularly important for emerging modalities, such as differential x-ray phase-contrast tomography (D-XPCT), which are currently limited by these factors. An important application of D-XPCT is high-resolution imaging of biomedical samples. However, reconstructing high-resolution images from few-view tomographic measurements remains a challenging task due to the high-frequency information loss caused by data incompleteness. In this work, a subspace-based reconstruction strategy is proposed and investigated for use in few-view D-XPCT image reconstruction. By adopting a two-step approach, the proposed method can simultaneously recover high-frequency details within a certain region of interest while suppressing noise and/or artifacts globally. The proposed method is investigated by the use of few-view experimental data acquired by an edge-illumination D-XPCT scanner

Mathematical Methods in Tomography

This is the seventh Oberwolfach conference on the mathematics of tomography, the first one taking place in 1980. Tomography is the most popular of a series of medical and scientific imaging techniques that have been developed since the mid seventies of the last century

The quantitative analysis of transonic flows by holographic interferometry

This thesis explores the feasibility of routine transonic flow analysis by holographic interferometry. Holography is potentially an important quantitative flow diagnostic, because whole-field data is acquired non-intrusively without the use of particle seeding. Holographic recording geometries are assessed and an image plane specular illumination configuration is shown to reduce speckle noise and maximise the depth-of-field of the reconstructed images. Initially, a NACA 0012 aerofoil is wind tunnel tested to investigate the analysis of two-dimensional flows. A method is developed for extracting whole-field density data from the reconstructed interferograms. Fringe analysis errors axe quantified using a combination of experimental and computer generated imagery. The results are compared quantitatively with a laminar boundary layer Navier-Stokes computational fluid dynamics (CFD) prediction. Agreement of the data is excellent, except in the separated wake where the experimental boundary layer has undergone turbulent transition. A second wind tunnel test, on a cone-cylinder model, demonstrates the feasibility of recording multi-directional interferometric projections using holographic optical elements (HOE’s). The prototype system is highly compact and combines the versatility of diffractive elements with the efficiency of refractive components. The processed interferograms are compared to an integrated Euler CFD prediction and it is shown that the experimental shock cone is elliptical due to flow confinement. Tomographic reconstruction algorithms are reviewed for analysing density projections of a three-dimensional flow. Algebraic reconstruction methods are studied in greater detail, because they produce accurate results when the data is ill-posed. The performance of these algorithms is assessed using CFD input data and it is shown that a reconstruction accuracy of approximately 1% may be obtained when sixteen projections are recorded over a viewing angle of ±58°. The effect of noise on the data is also quantified and methods are suggested for visualising and reconstructing obstructed flow regions

Quantitative electron microscopy for microstructural characterisation

Development of materials for high-performance applications requires accurate and useful analysis tools. In parallel with advances in electron microscopy hardware, we require analysis approaches to better understand microstructural behaviour. Such improvements in characterisation capability permit informed alloy design. New approaches to the characterisation of metallic materials are presented, primarily using signals collected from electron microscopy experiments. Electron backscatter diffraction is regularly used to investigate crystallography in the scanning electron microscope, and combined with energy-dispersive X-ray spectroscopy to simultaneusly investigate chemistry. New algorithms and analysis pipelines are developed to permit accurate and routine microstructural evaluation, leveraging a variety of machine learning approaches. This thesis investigates the structure and behaviour of Co/Ni-base superalloys, derived from V208C. Use of the presently developed techniques permits informed development of a new generation of advanced gas turbine engine materials.Open Acces

X-ray Phase Contrast Tomography : Setup and Scintillator Development

X-ray microscopy and micro-tomography (μCT) are valuable non-destructive examination methods in many disciplines such as bio-medical research, archaeometry, material science and paleontology. Besides being implemented at synchrotrons radiation sources, laboratory setups using an X-ray tube and high-resolution scintillation detector routinely provide information on the micrometre scale. To improve the image contrast for small and low-density samples, it is possible to introduce a propagation distance between sample and detector to perform propagation-based phase contrast imaging (PB-PCI). This contrast mode relies on a sufficiently coherent illumination and is characterised by the appearance of an additional intensity modulations (‘edge enhancement fringes’) around interfaces in the image. The strength of this effect depends on hardware as well as geometry parameters. This thesis describes the development of a laboratory setup for X-ray μCT with a PB-PCI option. It contains the theoretical and technical background of the setup design as well the characterization of the achieved performance.Moreover, the optimization of the PB-PCI geometry was explored both theoretically as well as experimentally for three different setups. A simple rule for finding the optimal magnification to achieve high phase contrast for edge features was deduced. The effect of the polychromatic source spectrum und detector sensitivity was identified and included into the theoretical model.Besides application and methodological studies, the setup was used to test and characterise new X-ray scintillator materials. Recently, metal halide perovskite nanocrystals (MHP NCs) have gained attention due to their outstanding opto-electronic performance. The main challenge for their use and commercialization is their low long-term stability against humidity, temperature, and light exposure. Here, a CsPbBr3 scintillator comprised of an ordered array of nanowires (NW) in an anodized aluminium oxide (AAO) membrane is presented as a promising new scintillator for X-ray microscopy and μCT. It shows a high light yield under X-ray exposure which improves with smaller NW diameter and higher NW length. In contrast to many other MHP materials this scintillator shows good stability under continuous X-ray exposure and changing environmental conditions over extended time spans of several weeks. This makes it suitable for tomography, which is demonstrated by acquiring the first high-resolution tomogram using a MHP scintillator with the presented laboratory setup

Novel ideas and techniques for large dark matter detectors

As dark matter detection experiments continue to report null results, the need for larger and more sensitive detectors means even more stringent design requirements. New calibration techniques are required and better calibration methods become possible with increased detector size. Additionally, previously ignored detector features such as convection become important, especially as internal, dissolvable sources become more common. Furthermore, convection also offers the possibility for reduction of the 222Rn backrounds via an offline analysis where atoms of 214Pb are tagged and followed throughout the detector via a technique dubbed the “radon self-veto”. In this thesis, we present the characterization of a deuterium-deuterium plasma fusion neutron generator optimized to perform the nuclear recoil calibration of XENON1T. Part of this characterization is done with liquid organic scintillator detectors, which are sensitive to both electonic and nuclear recoil interactions. We develop a new algorithm for discriminating between these two signal types using Laplace transforms and show that it performs better than traditional algorithms. A multipurpose source of dissolvable 220Rn is presented and measurements made of long-lived contaminants from this source. Finally, we present the first measurement of convection in XENON1T and report the results of a simple convection-agnostic implementation of the radon self-veto

Boosting the sensitivity of continuous gravitational waves all-sky searches using advanced filtering techniques

The work presented in this PhD thesis has been done in the context of gravitational-waves searches. Since the first detection on the 14th September 2015 by the LIGO-Virgo collaboration, a growing number of gravitational-wave events has been detected, all emitted by the coalescence of binary systems involving black holes and/or neutron stars. My work is focused on the search for continuous gravitational waves, which still miss the first detection. These signals are expected to be emitted, for instance, by spinning neutron stars with an asymmetric shape with respect to the rotation axis, and are at least five orders of magnitude weaker than the typical amplitude of detected binary coalescences. In this PhD thesis I report on the work done in four different projects, with the common purpose of increasing the sensitivity of continuous-wave searches, involving both data analysis and instrumental aspects. The first project is a contribution to the commissioning of the Virgo interferometer in view of the next observing run, O4, which will start in May 2023. My contribution has been mainly devoted to the noise hunting activity, focused on the identification and mitigation of instrumental-noise sources that can degrade the sensitivity of continuous-wave searches. The other three projects are related to data analysis. I have focused, in particular, on all-sky searches for sources without electromagnetic counterpart and long-lasting signals from rapidly evolving newly-born neutron stars. I have studied in great detail the robustness of an all-sky data analysis method in the case of overlapping signals. This is relevant for some exotic classes of continuous wave sources and, more generally, in view of third generation detectors, like Einstein Telescope. I have developed a two-dimensional filter, called triangular filter, to be applied to the search for long-lasting gravitational waves from unstable neutron stars, showing that thanks to this method an increase of the search sensitivity of about $20\%$ is achievable. Finally, I describe the first steps of a wide work to develop a new procedure for all-sky continuous-wave searches, exploiting a statistics based on the sidereal modulation, that affects astrophysical signals, due to the Earth rotation

Pattern Recognition and Event Reconstruction in Particle Physics Experiments

This report reviews methods of pattern recognition and event reconstruction used in modern high energy physics experiments. After a brief introduction into general concepts of particle detectors and statistical evaluation, different approaches in global and local methods of track pattern recognition are reviewed with their typical strengths and shortcomings. The emphasis is then moved to methods which estimate the particle properties from the signals which pattern recognition has associated. Finally, the global reconstruction of the event is briefly addressed.Comment: 101 pages, 58 figure

Digital Image Processing

Newspapers and the popular scientific press today publish many examples of highly impressive images. These images range, for example, from those showing regions of star birth in the distant Universe to the extent of the stratospheric ozone depletion over Antarctica in springtime, and to those regions of the human brain affected by Alzheimer’s disease. Processed digitally to generate spectacular images, often in false colour, they all make an immediate and deep impact on the viewer’s imagination and understanding. Professor Jonathan Blackledge’s erudite but very useful new treatise Digital Image Processing: Mathematical and Computational Methods explains both the underlying theory and the techniques used to produce such images in considerable detail. It also provides many valuable example problems - and their solutions - so that the reader can test his/her grasp of the physical, mathematical and numerical aspects of the particular topics and methods discussed. As such, this magnum opus complements the author’s earlier work Digital Signal Processing. Both books are a wonderful resource for students who wish to make their careers in this fascinating and rapidly developing field which has an ever increasing number of areas of application. The strengths of this large book lie in: • excellent explanatory introduction to the subject; • thorough treatment of the theoretical foundations, dealing with both electromagnetic and acoustic wave scattering and allied techniques; • comprehensive discussion of all the basic principles, the mathematical transforms (e.g. the Fourier and Radon transforms), their interrelationships and, in particular, Born scattering theory and its application to imaging systems modelling; discussion in detail - including the assumptions and limitations - of optical imaging, seismic imaging, medical imaging (using ultrasound), X-ray computer aided tomography, tomography when the wavelength of the probing radiation is of the same order as the dimensions of the scatterer, Synthetic Aperture Radar (airborne or spaceborne), digital watermarking and holography; detail devoted to the methods of implementation of the analytical schemes in various case studies and also as numerical packages (especially in C/C++); • coverage of deconvolution, de-blurring (or sharpening) an image, maximum entropy techniques, Bayesian estimators, techniques for enhancing the dynamic range of an image, methods of filtering images and techniques for noise reduction; • discussion of thresholding, techniques for detecting edges in an image and for contrast stretching, stochastic scattering (random walk models) and models for characterizing an image statistically; • investigation of fractal images, fractal dimension segmentation, image texture, the coding and storing of large quantities of data, and image compression such as JPEG; • valuable summary of the important results obtained in each Chapter given at its end; • suggestions for further reading at the end of each Chapter. I warmly commend this text to all readers, and trust that they will find it to be invaluable. Professor Michael J Rycroft Visiting Professor at the International Space University, Strasbourg, France, and at Cranfield University, England