各種の性質を改善した直交DTCWTの設計に関する研究

The Dual tree complex wavelet transforms (DTCWTs) have been found to be successful in many applications of signal and image processing. DTCWTs employ two real wavelet transforms, where one wavelet corresponds to the real part of complex wavelet and the other is the imaginary part. Two wavelet bases are required to be a Hilbert transform pair. Thus, DTCWTs are nearly shift invariant and have a good directional selectivity in two or higher dimensions with limited redundancies. In this dissertation, we propose two new classes of DTCWTs with improved properties. In Chapter 2, we review the Fourier transform at first and then introduce the fundamentals of dual tree complex wavelet transform. The wavelet transform has been proved to be a successful tool to express the signal in time and frequency domain simultaneously. To obtain the wavelet coefficients efficiently, the discrete wavelet transform has been introduced since it can be achieved by a tree of two-channel filter banks. Then, we discuss the design conditions of two-channel filter banks, i.e., the perfect reconstruction and orthonormality. Additionally, some properties of scaling and wavelet functions including orthonormality, symmetry and vanishing moments are also given. Moreover, the structure of DTCWT is introduced, where two wavelet bases are required to form a Hilbert transform pair. Thus, the corresponding scaling lowpass filters must satisfy the half-sample delay condition. Finally, the objective measures of quality are given to evaluate the performance of the complex wavelet. In Chapter 3, we propose a new class of DTCWTs with improved analyticity and frequency selectivity by using general IIR filters with numerator and denominator of different degree. In the common-factor technique proposed by Selesnick, the maximally at allpass filter was used to satisfy the halfsample delay condition, resulting in poor analyticity of complex wavelets. Thus, to improve the analyticity of complex wavelets, we present a method for designing allpass filters with the specified degree of flatness and equiripple phase response in the approximation band. Moreover, to improve the frequency selectivity of scaling lowpass filters, we locate the specified number of zeros at z = -1 and minimize the stopband error. The well-known Remez exchange algorithm has been applied to approximate the equiripple response. Therefore, a set of filter coefficients can be easily obtained by solving the eigenvalue problem. Furthermore, we investigate the performance on the proposed DTCWTs and dedicate how to choose the approximation band and stopband properly. It is shown that the conventional DTCWTs proposed by Selesnick are only the special cases of DTCWTs proposed in this dissertation. In Chapter 4, we propose another class of almost symmetric DTCWTs with arbitrary center of symmetry. We specify the degree of flatness of group delay, and the number of vanishing moments, then apply the Remez exchange algorithm to minimize the difference between two scaling lowpass filters in the frequency domain, in order to improve the analyticity of complex wavelets. Therefore, the equiripple behaviour of the error function can be obtained through a few iterations. Moreover, two scaling lowpass filters can be obtained simultaneously. As a result, the complex wavelets are orthogonal and almost symmetric, and have the improved analyticity. Since the group delay of scaling lowpass filters can be arbitrarily specified, the scaling functions have the arbitrary center of symmetry. Finally, several experiments of signal denoising are carried out to demonstrate the efficiency of the proposed DTCWTs. It is clear that the proposed DTCWTs can achieve better performance on noise reduction.電気通信大学201

Image Registration Workshop Proceedings

Automatic image registration has often been considered as a preliminary step for higher-level processing, such as object recognition or data fusion. But with the unprecedented amounts of data which are being and will continue to be generated by newly developed sensors, the very topic of automatic image registration has become and important research topic. This workshop presents a collection of very high quality work which has been grouped in four main areas: (1) theoretical aspects of image registration; (2) applications to satellite imagery; (3) applications to medical imagery; and (4) image registration for computer vision research

Wavelet Analysis of Nonstationary Circadian Time Series

Rhythmic data are ubiquitous in the life sciences, with biologists needing reliable statistical tools for the analysis of such data. When these signals display rhythmic yet nonstationary behaviour, common in many biological systems, the established methodologies are often misleading. Chapter 2 develops and tests a new method for clustering nonstationary rhythmic biological data. The method combines locally stationary wavelet time series modelling with functional principal components analysis and thus extracts time—scale patterns useful for identifying common characteristics. We demonstrate the advantages of our methodology over alternative approaches by means of a simulation study and for real circadian data applications. Motivated by three complementary applications in circadian biology, Chapter 3 develops new reliable statistical tests to identify whether a particular experimental treatment has caused a significant change in a rhythmic signal that displays nonstationary characteristics. As circadian behaviour is best understood in the spectral domain, we develop novel hypothesis testing procedures in the (wavelet) spectral domain, which facilitate the identification of three specific types of spectral difference. We demonstrate the advantages of our methodology over alternative approaches by means of a comprehensive simulation study and for real data applications, involving both plant and animal signals. Chapter 4 investigates the effect of industrial and agricultural pollutants on the plant circadian clock. We examine the impact of exposure to a comprehensive range of environmentally relevant pollutants by utilising the methodologies developed in Chapters 2 and 3. Our findings indicate that many of the tested chemicals have an effect on the plant circadian clock, most of which would have remained undetected by classical methods overlooking nonstationarity. The results of Chapter 4 demonstrate the additional insight gained by using the appropriate methodologies, as developed in Chapters 2 and 3, and also have important implications for understanding environmental ramifications associated with soil pollution

The 1995 Science Information Management and Data Compression Workshop

This document is the proceedings from the 'Science Information Management and Data Compression Workshop,' which was held on October 26-27, 1995, at the NASA Goddard Space Flight Center, Greenbelt, Maryland. The Workshop explored promising computational approaches for handling the collection, ingestion, archival, and retrieval of large quantities of data in future Earth and space science missions. It consisted of fourteen presentations covering a range of information management and data compression approaches that are being or have been integrated into actual or prototypical Earth or space science data information systems, or that hold promise for such an application. The Workshop was organized by James C. Tilton and Robert F. Cromp of the NASA Goddard Space Flight Center

UNSUPERVISED CLASSIFICATION OF HIGH-FREQUENCY OSCILLATIONS IN NEOCORTICAL EPILEPSY AND CONTROL PATIENTS

Quality of life for the more than 15 million people with drug-resistant epilepsy is tied to how precisely the brain areas responsible for generating their seizures can be localized. High-frequency (100-500 Hz) field-potential oscillations (HFOs) are emerging as a candidate biomarker for epileptogenic networks, but quantitative HFO studies are hampered by selection bias arising out of the need to reduce large volumes of data in the absence of capable automated processing methods. In this thesis, I introduce and evaluate an algorithm for the automatic detection and classification of HFOs that can be deployed without human intervention across long, continuous data records from large numbers of patients. I then use the algorithm in analyzing unique macro- and microelectrode intracranial electroencephalographic recordings from human neocortical epilepsy patients and controls. A central finding is that one class of HFOs discovered by the algorithm (median bandpassed spectral centroid ~140 Hz) is more prevalent in the seizure onset zone than outside. The outcomes of this work add to our understanding of epileptogenic networks and are suitable for near-term translation into improved surgical and device-based treatments

Single atom imaging with time-resolved electron microscopy

Developments in scanning transmission electron microscopy (STEM) have opened up new possibilities for time-resolved imaging at the atomic scale. However, rapid imaging of single atom dynamics brings with it a new set of challenges, particularly regarding noise and the interaction between the electron beam and the specimen. This thesis develops a set of analytical tools for capturing atomic motion and analyzing the dynamic behaviour of materials at the atomic scale. Machine learning is increasingly playing an important role in the analysis of electron microscopy data. In this light, new unsupervised learning tools are developed here for noise removal under low-dose imaging conditions and for identifying the motion of surface atoms. The scope for real-time processing and analysis is also explored, which is of rising importance as electron microscopy datasets grow in size and complexity. These advances in image processing and analysis are combined with computational modelling to uncover new chemical and physical insights into the motion of atoms adsorbed onto surfaces. Of particular interest are systems for heterogeneous catalysis, where the catalytic activity can depend intimately on the atomic environment. The study of Cu atoms on a graphene oxide support reveals that the atoms undergo anomalous diffusion as a result of spatial and energetic disorder present in the substrate. The investigation is extended to examine the structure and stability of small Cu clusters on graphene oxide, with atomistic modelling used to understand the significant role played by the substrate. Finally, the analytical methods are used to study the surface reconstruction of silicon alongside the electron beam-induced motion of adatoms on the surface. Taken together, these studies demonstrate the materials insights that can be obtained with time-resolved STEM imaging, and highlight the importance of combining state-ofthe- art imaging with computational analysis and atomistic modelling to quantitatively characterize the behaviour of materials with atomic resolution.The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement 291522–3DIMAGE, as well as from the European Union Seventh Framework Programme under Grant Agreement 312483-ESTEEM2 (Integrated Infrastructure Initiative -I3)

Accurate cosmology with galaxy and quasar surveys

Observations of the cosmic microwave background have led to a golden age of cosmology, where precise measurements can be confronted with predictions from cosmological models. Ongoing and future surveys of the distribution of galaxies will continue this revolution: they will enable us to test the laws of gravity, uncover the properties of dark energy and dark matter, and reinforce the connection to high-energy physics. However, current galaxy survey analyses are already limited by our ability to identify and treat observational systematics, and this problem will be even more pronounced in future experiments. Therefore, it is essential to develop novel methods to deal with these complications when testing cosmological models and searching for new physics. This is the focus of this thesis. Firstly, I will present measurements of primordial non-Gaussianity obtained from the clustering of quasars from the Sloan Digital Sky Survey. Primordial non-Gaussianity is a powerful probe of inflation, the leading theory of the initial conditions of the universe, but its effects on the distribution of quasars are mimicked by observational systematics. I will describe a framework to deal with these systematics and robustly measure primordial non-Gaussianity from the clustering of quasars. Secondly, I will present a new set of wavelet transforms on the sphere and the ball. These approaches are highly promising for analysing cosmological and geophysical data and dealing with their systematics in novel ways. Finally, I will examine the recent claims that extra massive neutrinos can resolve the tensions between cosmic microwave background, galaxy survey and supernova observations. I will demon- strate that this conclusion is premature since it is driven by the least robust data sets. Given the growing number of cosmological observables and their varied levels of robustness, combining data sets and dealing with such tensions will become critical in the near future