Recent advances in x-ray cone-beam computed laminography

X-ray computed tomography is a well established volume imaging technique used routinely in medical diagnosis, industrial non-destructive testing, and a wide range of scientific fields. Traditionally, computed tomography uses scanning geometries with a single axis of rotation together with reconstruction algorithms specifically designed for this setup. Recently there has however been increasing interest in more complex scanning geometries. These include so called X-ray computed laminography systems capable of imaging specimens with large lateral dimensions, or large aspect ratios, neither of which are well suited to conventional CT scanning procedures. Developments throughout this field have thus been rapid, including the introduction of novel system trajectories, the application and refinement of various reconstruction methods, and the use of recently developed computational hardware and software techniques to accelerate reconstruction times. Here we examine the advances made in the last several years and consider their impact on the state of the art

Mathematics and Algorithms in Tomography

This is the eighth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, sonar, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, vector tomography, and texture analysis

Bayesian Methods for Gas-Phase Tomography

Gas-phase tomography refers to a set of techniques that determine the 2D or 3D distribution of a target species in a jet, plume, or flame using measurements of light, made around the boundary of a flow area. Reconstructed quantities may include the concentration of one or more species, temperature, pressure, and optical density, among others. Tomography is increasingly used to study fundamental aspects of turbulent combustion and monitor emissions for regulatory compliance. This thesis develops statistical methods to improve gas-phase tomography and reports two novel experimental applications. Tomography is an inverse problem, meaning that a forward model (calculating measurements of light for a known distribution of gas) is inverted to estimate the model parameters (transforming experimental data into a gas distribution). The measurement modality varies with the problem geometry and objective of the experiment. For instance, transmittance data from an array of laser beams that transect a jet may be inverted to recover 2D fields of concentration and temperature; and multiple high-resolution images of a flame, captured from different angles, are used to reconstruct wrinkling of the 3D reacting zone. Forward models for gas-phase tomography modalities share a common mathematical form, that of a Fredholm integral equation of the first-kind (IFK). The inversion of coupled IFKs is necessarily ill-posed, however, meaning that solutions are either unstable or non-unique. Measurements are thus insufficient in themselves to generate a realistic image of the gas and additional information must be incorporated into the reconstruction procedure. Statistical inversion is an approach to inverse problems in which the measurements, experimental parameters, and quantities of interest are treated as random variables, characterized by a probability distribution. These distributions reflect uncertainty about the target due to fluctuations in the flow field, noise in the data, errors in the forward model, and the ill-posed nature of reconstruction. The Bayesian framework for tomography features a likelihood probability density function (pdf), which describes the chance of observing a measurement for a given distribution of gas, and prior pdf, which assigns a relative plausibility to candidate distributions based on assumptions about the flow physics. Bayes’ equation updates information about the target in response to measurement data, combining the likelihood and prior functions to form a posterior pdf. The posterior is usually summarized by the maximum a posteriori (MAP) estimate, which is the most likely distribution of gas for a set of data, subject to the effects of noise, model errors, and prior information. The framework can be used to estimate credibility intervals for a reconstruction and the form of Bayes’ equation suggests procedures for improving gas tomography. The accuracy of reconstructions depends on the information content of the data, which is a function of the experimental design, as well as the specificity and validity of the prior. This thesis employs theoretical arguments and experimental measurements of scalar fluctuations to justify joint-normal likelihood and prior pdfs for gas-phase tomography. Three methods are introduced to improve each stage of the inverse problem: to develop priors, design optimal experiments, and select a discretization scheme. First, a self-similarity analysis of turbulent jets—common targets in gas tomography—is used to construct an advanced prior, informed by an estimate of the jet’s spatial covariance. Next, a Bayesian objective function is proposed to optimize beam positions in limited-data arrays, which are necessary in scenarios where optical access to the flow area is restricted. Finally, a Bayesian expression for model selection is derived from the joint-normal pdfs and employed to select a mathematical basis to reconstruct a flow. Extensive numerical evidence is presented to validate these methods. The dissertation continues with two novel experiments, conducted in a Bayesian way. Broadband absorption tomography is a new technique intended for quantitative emissions detection from spectrally-convolved absorption signals. Theoretical foundations for the diagnostic are developed and the results of a proof-of-concept emissions detection experiment are reported. Lastly, background-oriented schlieren (BOS) tomography is applied to combustion for the first time. BOS tomography employs measurements of beam steering to reconstruct a fluid’s optical density field, which can be used to infer temperature and density. The application of BOS tomography to flame imaging sets the stage for instantaneous 3D combustion thermometry. Numerical and experimental results reported in this thesis support a Bayesian approach to gas-phase tomography. Bayesian tomography makes the role of prior information explicit, which can be leveraged to optimize reconstructions and design better imaging systems in support of research on fluid flow and combustion dynamics

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation: Part B-Defects Imaging and Recognition Techniques

The wavefield of Lamb waves is yielded by the feature of plate-like structures. And many defects imaging techniques and intelligent recognition algorithms have been developed for defects location, sizing and recognition through analyzing the parameters of received Lamb waves signals including the arrival time, attenuation, amplitude and phase, etc. In this chapter, we give a briefly review about the defects imaging techniques and the intelligent recognition algorithms. Considering the available parameters of Lamb waves signals and the setting of detection/monitoring systems, we roughly divide the defect location and sizing techniques into four categories, including the sparse array imaging techniques, the tomography techniques, the compact array techniques, and full wavefield imaging techniques. The principle of them is introduced. Meanwhile, the intelligent recognition techniques based on various of intelligent recognition algorithms that have been widely used to analyze Lamb waves signals in the research of defect recognition are reviewed, including the support vector machine, Bayesian methodology, and the neural networks

On random tomography with unobservable projection angles

We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in random and unobservable directions. Such a problem is distinct from the classic problem of tomography where both the projections and the unit vectors normal to the projection plane are observable. The problem arises in single particle electron microscopy, a powerful method that biophysicists employ to learn the structure of biological macromolecules. Strictly speaking, the problem is unidentifiable and an appropriate reformulation is suggested hinging on ideas from Kendall's theory of shape. Within this setup, we demonstrate that a consistent solution to the problem may be derived, without attempting to estimate the unknown angles, if the density is assumed to admit a mixture representation.Comment: Published in at http://dx.doi.org/10.1214/08-AOS673 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Wavelet transform and terahertz local tomography

Copyright © 2007 SPIE - The International Society for Optical Engineering. Copyright 2007 Society of Photo-Optical Instrumentation Engineers. This paper was published in Novel Optical Instrumentation for Biomedical Applications III, edited by Christian D. Depeursinge Proc. of SPIE-OSA Biomedical Optics, SPIE Vol. 6631, 663113 and is made available as an electronic reprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.We use the theory of two dimensional discrete wavelet transforms to derive inversion formulas for the Radon transform of terahertz datasets. These inversion formulas with good localised properties are implemented for the reconstruction of terahertz imaging in the area of interest, with a significant reduction in the required measurements. As a form of optical coherent tomography, terahertz CT complements the current imaging techniques and offers a promising approach for achieving non-invasive inspection of solid materials, with potentially numerous applications in industrial manufacturing and biomedical engineering. © 2007 SPIE-OSA.Xiaoxia Yin and Brian W.-H. Ng and Bradley Fergusona and Derek Abbot