Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective

Bibliography: p. 208-225.Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques

Spike detection using the continuous wavelet transform

This paper combines wavelet transforms with basic detection theory to develop a new unsupervised method for robustly detecting and localizing spikes in noisy neural recordings. The method does not require the construction of templates, or the supervised setting of thresholds. We present extensive Monte Carlo simulations, based on actual extracellular recordings, to show that this technique surpasses other commonly used methods in a wide variety of recording conditions. We further demonstrate that falsely detected spikes corresponding to our method resemble actual spikes more than the false positives of other techniques such as amplitude thresholding. Moreover, the simplicity of the method allows for nearly real-time execution

GNSS interference management techniques against malicious attacks

This thesis collects the outcomes of a Ph.D. course in Telecommunications Engineering and it is focused on the study and design of possible techniques able to counteract interference signal in Global Navigation Satellite System (GNSS) systems. The subject is the jamming threat in navigation systems, that has become a very increasingly important topic in recent years, due to the wide diffusion of GNSS-based civil applications. Detection and mitigation techniques are developed in order to fight out jamming signals, tested in different scenarios and including sophisticated signals. The thesis is organized in two main parts, which deal with management of GNSS intentional counterfeit signals. The first part deals with the interference management, focusing on the intentional interfering signal. In particular, a technique for the detection and localization of the interfering signal level in the GNSS bands in frequency domain has been proposed. In addition, an effective mitigation technique which exploits the periodic characteristics of the common jamming signals reducing interfering effects at the receiver side has been introduced. Moreover, this technique has been also tested in a different and more complicated scenario resulting still effective in mitigation and cancellation of the interfering signal, without high complexity. The second part still deals with the problem of interference management, but regarding with more sophisticated signal. The attention is focused on the detection of spoofing signal, which is the most complex among the jamming signal types. Due to this highly difficulty in detect and mitigate this kind of signal, spoofing threat is considered the most dangerous. In this work, a possible techniques able to detect this sophisticated signal has been proposed, observing and exploiting jointly the outputs of several operational block measurements of the GNSS receiver operating chain

Measurements, Models, Systems and Design

531 s.

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Enhancing the performance of spread spectrum techniques in different applications

Spread spectrum, Automotive Radar, Indoor Positioning Systems, Ultrasonic and Microwave Imaging, super resolution technique and wavelet transformMagdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2006von Omar Abdel-Gaber Mohamed Al

Data-driven time-frequency analysis of multivariate data

Empirical Mode Decomposition (EMD) is a data-driven method for the decomposition and time-frequency analysis of real world nonstationary signals. Its main advantages over other time-frequency methods are its locality, data-driven nature, multiresolution-based decomposition, higher time-frequency resolution and its ability to capture oscillation of any type (nonharmonic signals). These properties have made EMD a viable tool for real world nonstationary data analysis. Recent advances in sensor and data acquisition technologies have brought to light new classes of signals containing typically several data channels. Currently, such signals are almost invariably processed channel-wise, which is suboptimal. It is, therefore, imperative to design multivariate extensions of the existing nonlinear and nonstationary analysis algorithms as they are expected to give more insight into the dynamics and the interdependence between multiple channels of such signals. To this end, this thesis presents multivariate extensions of the empirical mode de- composition algorithm and illustrates their advantages with regards to multivariate non- stationary data analysis. Some important properties of such extensions are also explored, including their ability to exhibit wavelet-like dyadic filter bank structures for white Gaussian noise (WGN), and their capacity to align similar oscillatory modes from multiple data channels. Owing to the generality of the proposed methods, an improved multi- variate EMD-based algorithm is introduced which solves some inherent problems in the original EMD algorithm. Finally, to demonstrate the potential of the proposed methods, simulations on the fusion of multiple real world signals (wind, images and inertial body motion data) support the analysis

Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

Intelligent detectors

Die vorliegende Arbeit stellt eine Basis zur Entwicklung von On-Board Software für astronomische Satelliten dar. Sie dient als Anleitung und Nachschlagewerk und zeigt anhand der Projekte Herschel/PACS und SPICA/SAFARI, wie aus den Grundlagen weltraumtaugliche Flugsoftware entsteht. Dazu gehören das Verstehen des wissenschaftlichen Zwecks, also was soll wie gemessen werden und wofür ist das gut, sowie die Kenntnis der physikalischen Eigenschaften des Detektors, das Beherrschen der mathematischen Operationen zur Verarbeitung der Daten und natürlich auch die Berücksichtigung der Umstände, unter welchen der Detektor zum Einsatz kommt.This thesis contains the knowledge and a good deal of experience that are necessary for the development of such astronomical on-board software for satellites. The key elements in the development are the understanding of the scientific purpose, knowledge of the physical properties of the detector, the comprehension of the mathematical operations involved in data processing and the consideration of the technical and observational circumstances