Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior

Enhancement of Single and Composite Images Based on Contourlet Transform Approach

Image enhancement is an imperative step in almost every image processing algorithms. Numerous image enhancement algorithms have been developed for gray scale images despite their absence in many applications lately. This thesis proposes hew image enhancement techniques of 8-bit single and composite digital color images. Recently, it has become evident that wavelet transforms are not necessarily best suited for images. Therefore, the enhancement approaches are based on a new 'true' two-dimensional transform called contourlet transform. The proposed enhancement techniques discussed in this thesis are developed based on the understanding of the working mechanisms of the new multiresolution property of contourlet transform. This research also investigates the effects of using different color space representations for color image enhancement applications. Based on this investigation an optimal color space is selected for both single image and composite image enhancement approaches. The objective evaluation steps show that the new method of enhancement not only superior to the commonly used transformation method (e.g. wavelet transform) but also to various spatial models (e.g. histogram equalizations). The results found are encouraging and the enhancement algorithms have proved to be more robust and reliable

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images

Statistical Characterization of Morphodynamic Signals Using Wavelet Analysis

Morphodynamic and hydrodynamic properties are concomitantly part of the entire dynamic of river systems and commonly present both temporal and spatial persistent variability. Therefore, the study of both river morphodynamic signals (e.g. bed forms and meandering and anabranching river morphometrics) and hydrodynamic signals (e.g. velocity fields, sediment concentrations) requires both temporal and spatial multi-scale signal representations. The present research is focused on the former type of signals and it is a first attempt to discriminate such signals and, subsequently, develop the theoretical background to link these processes at different spatial and temporal scales and determine the scales that have more influence on river evolution. The main contribution of this study are: [1] to design a methodology to discriminate bed form features (e.g. bars, dunes and ripples) via the combined application of robust spline filters and one-dimensional continuous wavelet transforms, allowing the quantitative recognition of bed form hierarchies. The methodology was tested by using synthetic bed form signals and subsequently applied to the analysis of bed form features from the Parana River, Argentina. [2] To develop a methodology for the statistical analysis of the spatial distribution of meandering rivers morphometrics by coupling the capabilities of one-dimensional wavelet transforms, principal component analysis and Frechet distance. A universal river classification method is also proposed. [3] To perform a novel study of the planimetric configuration of confluences in tropical free meandering rivers located in the upper Amazon catchment. River confluences in tropical environments represent areas where biota is concentrated; therefore, a better understanding and characterization of these features has a particular importance for the Amazonian ecosystem. [4] To evaluate the potential of two-dimensional wavelet transforms in the analysis of bed form features. The broader impact will be an improved understanding of river morphodynamics of the upper Amazon River for practical applications such as navigability. Furthermore, the project will provide an updated statistical analysis of the meandering rivers dynamics for practical applications, including erosion control, river ecology, and habitat restoration. The developed statistical tool will be included as an application of the RVR Meander platform (www.rvrmeander.org), which is a broadly used software for river restoration

Enhancement of Single and Composite Images Based on Contourlet Transform Approach

Image enhancement is an imperative step in almost every image processing algorithms. Numerous image enhancement algorithms have been developed for gray scale images despite their absence in many applications lately. This thesis proposes hew image enhancement techniques of 8-bit single and composite digital color images. Recently, it has become evident that wavelet transforms are not necessarily best suited for images. Therefore, the enhancement approaches are based on a new 'true' two-dimensional transform called contourlet transform. The proposed enhancement techniques discussed in this thesis are developed based on the understanding of the working mechanisms of the new multiresolution property of contourlet transform. This research also investigates the effects of using different color space representations for color image enhancement applications. Based on this investigation an optimal color space is selected for both single image and composite image enhancement approaches. The objective evaluation steps show that the new method of enhancement not only superior to the commonly used transformation method (e.g. wavelet transform) but also to various spatial models (e.g. histogram equalizations). The results found are encouraging and the enhancement algorithms have proved to be more robust and reliable

Pattern Recognition

A wealth of advanced pattern recognition algorithms are emerging from the interdiscipline between technologies of effective visual features and the human-brain cognition process. Effective visual features are made possible through the rapid developments in appropriate sensor equipments, novel filter designs, and viable information processing architectures. While the understanding of human-brain cognition process broadens the way in which the computer can perform pattern recognition tasks. The present book is intended to collect representative researches around the globe focusing on low-level vision, filter design, features and image descriptors, data mining and analysis, and biologically inspired algorithms. The 27 chapters coved in this book disclose recent advances and new ideas in promoting the techniques, technology and applications of pattern recognition

Digital forensic techniques for the reverse engineering of image acquisition chains

In recent years a number of new methods have been developed to detect image forgery. Most forensic techniques use footprints left on images to predict the history of the images. The images, however, sometimes could have gone through a series of processing and modification through their lifetime. It is therefore difficult to detect image tampering as the footprints could be distorted or removed over a complex chain of operations. In this research we propose digital forensic techniques that allow us to reverse engineer and determine history of images that have gone through chains of image acquisition and reproduction. This thesis presents two different approaches to address the problem. In the first part we propose a novel theoretical framework for the reverse engineering of signal acquisition chains. Based on a simplified chain model, we describe how signals have gone in the chains at different stages using the theory of sampling signals with finite rate of innovation. Under particular conditions, our technique allows to detect whether a given signal has been reacquired through the chain. It also makes possible to predict corresponding important parameters of the chain using acquisition-reconstruction artefacts left on the signal. The second part of the thesis presents our new algorithm for image recapture detection based on edge blurriness. Two overcomplete dictionaries are trained using the K-SVD approach to learn distinctive blurring patterns from sets of single captured and recaptured images. An SVM classifier is then built using dictionary approximation errors and the mean edge spread width from the training images. The algorithm, which requires no user intervention, was tested on a database that included more than 2500 high quality recaptured images. Our results show that our method achieves a performance rate that exceeds 99% for recaptured images and 94% for single captured images.Open Acces

Local Geometric Transformations in Image Analysis

The characterization of images by geometric features facilitates the precise analysis of the structures found in biological micrographs such as cells, proteins, or tissues. In this thesis, we study image representations that are adapted to local geometric transformations such as rotation, translation, and scaling, with a special emphasis on wavelet representations. In the first part of the thesis, our main interest is in the analysis of directional patterns and the estimation of their location and orientation. We explore steerable representations that correspond to the notion of rotation. Contrarily to classical pattern matching techniques, they have no need for an a priori discretization of the angle and for matching the filter to the image at each discretized direction. Instead, it is sufficient to apply the filtering only once. Then, the rotated filter for any arbitrary angle can be determined by a systematic and linear transformation of the initial filter. We derive the Cramér-Rao bounds for steerable filters. They allow us to select the best harmonics for the design of steerable detectors and to identify their optimal radial profile. We propose several ways to construct optimal representations and to build powerful and effective detector schemes; in particular, junctions of coinciding branches with local orientations. The basic idea of local transformability and the general principles that we utilize to design steerable wavelets can be applied to other geometric transformations. Accordingly, in the second part, we extend our framework to other transformation groups, with a particular interest in scaling. To construct representations in tune with a notion of local scale, we identify the possible solutions for scalable functions and give specific criteria for their applicability to wavelet schemes. Finally, we propose discrete wavelet frames that approximate a continuous wavelet transform. Based on these results, we present a novel wavelet-based image-analysis software that provides a fast and automatic detection of circular patterns, combined with a precise estimation of their size

Self-Similar Vector Fields

We propose statistically self-similar and rotation-invariant models for vector fields, study some of the more significant properties of these models, and suggest algorithms and methods for reconstructing vector fields from numerical observations, using the same notions of self-similarity and invariance that give rise to our stochastic models. We illustrate the efficacy of the proposed schemes by applying them to the problems of denoising synthetic flow phantoms and enhancing flow-sensitive magnetic resonance imaging (MRI) of blood flow in the aorta. In constructing our models and devising our applied schemes and algorithms, we rely on two fundamental notions. The first of these, referred to as "innovation modelling" in the thesis, is the principle —applicable both analytically and synthetically— of reducing complex phenomena to combinations of simple independent components or "innovations". The second fundamental idea is that of "invariance", which indicates that in the absence of any distinguishing factor, two equally valid models or solutions should be given equal consideration