Virus recognition by visual examination of electron microscope (EM) images is time consuming and requires highly trained and experienced medical specialists. For these reasons, it is not suitable for screening large numbers of specimens. The objective of this research was to develop a reliable and robust pattern recognition system that could be trained to detect and classify different types of viruses from two-dimensional images obtained from an EM. This research evaluated the use of radial spectra of higher order spectral invariants to capture variations in textures and differences in symmetries of different types of viruses in EM images. The technique exploits invariant properties of the higher order spectral features, statistical techniques of feature averaging, and soft decision fusion in a unique manner applicable to the problem when a large number of particles were available for recognition, but were not easily registered on an individual basis due to the low signal to noise ratio. Experimental evaluations were carried out using EM images of viruses, and a high statistical reliability with low misclassification rates was obtained, showing that higher order spectral features are effective in classifying viruses from digitized electron micrographs. With the use of digital imaging in electron microscopes, this method can be fully automated.

The cosmic microwave background (CMB) provides unprecedented details about the history of our universe and helps to establish the standard model in modern cosmology. With the ongoing and future CMB observations, higher precision can be achieved and novel windows will be opened for studying different phenomena. Non-Gaussianity is one of the most exciting effects which fascinate many cosmologists. While numerous alternative inflationary models predict detectable primordial non-Gaussianities generated during inflation, the single-field slow-roll inflation of the standard model is known to produce negligible non-Gaussianities. However, post-inflationary processes guarantee the generation of non-Gaussianities through the nonlinear evolution of our universe after inflation, regardless of the underlying inflationary theory. These non-Gaussianities not only may contaminate the potential primordial non-Gaussian signals, but also may offer independent tests for late-time physics (such as General Relativity). Therefore, it is of great interest to study them quantitatively. In this thesis, we will study the post-inflationary non-Gaussianities in two main aspects. First, we calculate the CMB bispectrum imprinted by the 2nd-order perturbations during recombination. We carry out a numerical calculation including all the dominant effects at recombination and separate them consistently from the late-time effects. We find that the recombination bispectrum is subdominant compared to the ISW-lensing bispectrum. Although the effect will not be detectable for the Planck mission, its signal-to-noise is large enough that they present themselves as systematics. Thus, it has to be taken into account in future experiments. Second, we formulate the lensing, redshift and time-delay effects through the Boltzmann equation. The new formalism allows us to explicitly list out all the approximations implied in the canonical remapping approach. In particular, we quantify the correction of the CMB temperature power spectrum from the lens-lens couplings and confirm that the correction is small.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20908号 / 理博第4360号 / 新制||理||1626(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 樽家 篤史, 教授 佐々木 節, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Title: Testing for linearity in time series Author: Martin Melicherčík Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zuzana Prášková, CSc., Department of Probability and Mathematical Statistics Abstract: In the first part of the thesis, a necessary theoretical base from time series analysis is explained, which is consequently used to formulate several tests for linearity. According to variety of approaches the theory includes wide range of knowledge from correlation and spectral analysis and introduces some basic nonlinear models. In the second part, linearity tests are described, classified and compared both theoretically and practically on simulated data from several linear and nonlinear models. At the end, some scripts and hints in R language are introduced that could be used when applying tests to real data. Keywords: linear time series, bispectrum, testing for linearity, nonlinear models

In this thesis, rotation, scale and translation (RST) invariant automatic target recognition (ATR) for satellite imagery is presented. Template matching is used to realize the target recognition. However, unlike most of the studies of template matching in the literature, RST invariance is required in our problem, since most of the time we will have only a small number of templates of each target, while the targets to be recognized in the scenes will have various orientations, scaling and translations. RST invariance is studied in detail and implemented with some of the competing methods in the literature, such as Fourier-Mellin transform and bipectrum combined with log-polar mapping. Phase correlation and normalized cross-correlation are used as similarity metrics. Encountered drawbacks were overcome with additional operations and modifications of the algorithms. ATR using reconstruction of the target image with respect to the template, based on bispectrum, log-polar mapping and phase correlation outperformed the other methods and successful recognition was realized for various target types, especially for targets on relatively simpler backgrounds, i.e. containing little or no other objects.

Abstract Pattern recognition and registration are integral elements of computer vision, which considers image patterns. This thesis presents novel blur, and combined blur and geometric invariant features for pattern recognition and registration related to images. These global or local features are based on the Fourier transform phase, and are invariant or insensitive to image blurring with a centrally symmetric point spread function which can result, for example, from linear motion or out of focus. The global features are based on the even powers of the phase-only discrete Fourier spectrum or bispectrum of an image and are invariant to centrally symmetric blur. These global features are used for object recognition and image registration. The features are extended for geometrical invariances up to similarity transformation: shift invariance is obtained using bispectrum, and rotation-scale invariance using log-polar mapping of bispectrum slices. Affine invariance can be achieved as well using rotated sets of the log-log mapped bispectrum slices. The novel invariants are shown to be more robust to additive noise than the earlier blur, and combined blur and geometric invariants based on image moments. The local features are computed using the short term Fourier transform in local windows around the points of interest. Only the lowest horizontal, vertical, and diagonal frequency coefficients are used, the phase of which is insensitive to centrally symmetric blur. The phases of these four frequency coefficients are quantized and used to form a descriptor code for the local region. When these local descriptors are used for texture classification, they are computed for every pixel, and added up to a histogram which describes the local pattern. There are no earlier textures features which have been claimed to be invariant to blur. The proposed descriptors were superior in the classification of blurred textures compared to a few non-blur invariant state of the art texture classification methods.

Higher-order spectral analysis of acoustical waveforms can provide phase information that is not retained in calculations of power spectral density. In the propagation of high intensity sound, nonlinearity can cause substantial changes in the waveform as frequency components interact with one another. The bispectrum, which is one order higher than power spectral density, may provide a useful measure of nonlinearity in propagation by highlighting spectral regions of interaction. This thesis provides a review of the bispectrum, places it in the context of nonlinear acoustic propagation, and presents spectra calculated as a function of distance for numerically propagated acoustic waveforms. The calculated spectra include power spectral density, quad-spectral density, bispectrum, spatial derivative of the bispectrum, bicoherence, and skewness function. / text

One of the most significant goals in coal mining technology research is the automation of underground coal mining machinery. A current challenge with automating underground coal mining machinery is measuring and maintaining a coal mining horizon. The coal mining horizon is the horizontal path the machinery follows through the undulating coal seam during the mining operation. A typical mining practice is to leave a thin remnant of coal unmined in order to maintain geological stability of the cutting face. If the remnant layer is too thick, resources are wasted as the unmined coal is permanently unrecoverable. If the remnant layer is too thin, the product is diluted by mining into the overburden and there is an increased risk of premature roof fall which increases danger. The main challenge therefore is to develop a robust sensing method to estimate the thickness of thin remant coal layers. This dissertation addresses this challenge by presenting a pattern recognition methodology to estimate thin remnant coal layer thickness using ground penetrating radar (GPR). The approach is based upon a novel feature vector, derived from the bispectrum, that is used to characterise the early-time segment of 1D GPR data. The early-time segment is dominated by clutter inherent in GPR systems such as antenna crosstalk, ringdown and ground-bounce. It is common practice to either time-gate the signal, disregard the clutter by rendering the early-time segment unusable, or configure the GPR equipment to minimise the clutter effects which in turn reduces probing range. Disregarding the early-time signal essentially imposes a lower thickness limit on traditional GPR layer thickness estimators. The challenges of estimating thin layer thickness is primarily due to these inherent clutter components. Traditional processing strategies attempt to minimise the clutter using pre-processing techniques such as the subtraction of a calibration signal. The proposed method, however, treats the clutter as a deterministic but unknown signal with additive noise. Hence the proposed approach utilises the energy from the clutter and monitors change in media from subtle changes in the signal shape. Two complementary processing methods important to horizon sensing have been also proposed. These methods, near-surface interface detection and antenna height estimation, may be used as pre-validation tools to increase the robustness of the thickness estimation technique. The proposed methods have been tested with synthetic data and validated with real data obtained using a low power 1.4 GHz GPR system and a testbed with known conditions. With the given test system, it is shown that the proposed thin layer thickness estimator and near-surface interface detector outperform the traditional matched filter based processing methods for layers less than 5 cm in thickness. It is also shown that the proposed antenna height estimator outperforms the traditional height estimator for heights less than 7 cm. These new methods provide a means for reliably extending layer thickness estimation to the thin layer case where traditional approaches are known to fail.

Much of the recent progress in cosmology has come from studying the power spectrum of the cosmic microwave background (CMB). The latest results from the Planck satellite confirmed that the inflationary paradigm with the $\Lambda$CDM six-parameter model provides a very good description of the observed structures in the Universe. Even so, additional parameters, such as cosmic defects, are still allowed by current observational data. Additionally, many of the inflationary models predict a significant departure from Gaussianity in the distribution of primordial perturbations. Higher order statistics, such as the bispectrum, are required to test and constrain such models. The late-time distribution of matter in the Universe - large-scale structure (LSS) - contains much more information than the CMB that has not yet been used. In this thesis, we look at both problems: the effects of cosmic defects, in particular cosmic strings and domain walls on the CMB power spectrum through numerical simulations, and the dark matter bispectrum of large-scale structure. Topological defects are predicted by most inflationary theories involving symmetry breaking in the early Universe. In this thesis we study the effects of cosmic strings and domain walls on the CMB by determining their power spectrum. We use Nambu-Goto and field theory simulations for cosmic strings and domain walls respectively, and we determine the power spectra they produce with a modified Einstein-Boltzmann solver sourced by unequal time correlators from components of the energy-momentum tensor of the defects. We use these spectra together with CMB likelihoods to obtain constraints on the energy scales of formation of the cosmic defects, finding $G\mu/c^{2} < 1.29 \times 10^{−7}$ and $\eta < 0.93$ MeV (at 95% confidence level) for cosmic strings and domain walls respectively, when using the Planck satellite likelihoods. For the matter bispectrum of LSS, we compare different perturbative and phenomenological models with measurements from $N$-body simulations by using shape and amplitude correlators and we determine on which scales and for which redshifts they are accurate. We propose a phenomenological ‘three-shape’ model, based on the fundamental shapes we have observed by studying the halo model that are also present in the simulations. When calibrated on the simulations, this model accurately describes the bispectrum on all scales and redshifts considered, providing a prototype bispectrum HALOFIT-like methodology that could be used to describe and test parameter dependencies.

In this study, we present two new frequency domain tests for testing the Gaussianity and linearity of a sixth-order stationary univariate time series. Both are two-stage tests. The first stage is a test for the Gaussianity of the series. Under Gaussianity, the estimated normalized bispectrum has an asymptotic chi-square distribution with two degrees of freedom. If Gaussianity is rejected, the test proceeds to the second stage, which tests for linearity. Under linearity, with non-Gaussian errors, the estimated normalized bispectrum has an asymptotic non-central chi-square distribution with two degrees of freedom and constant noncentrality parameter. If the process is nonlinear, the noncentrality parameter is nonconstant. At each stage, empirical distribution function (EDF) goodness-ofit (GOF) techniques are applied to the estimated normalized bispectrum by comparing the empirical CDF with the appropriate null asymptotic distribution. The two specific methods investigated are the Anderson-Darling and Cramer-von Mises tests. Under Gaussianity, the distribution is completely specified, and application is straight forward. However, if Gaussianity is rejected, the proposed application of the EDF tests involves a transformation to normality. The performance of the tests and a comparison of the EDF tests to existing time and frequency domain tests are investigated under a variety of circumstances through simulation. For illustration, the tests are applied to a number of data sets popular in the time series literature.