Approximation algorithms for wavelet transform coding of data streams

This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance between f and its representation. The first known algorithms for finding provably approximate representations minimizing general $\ell_p$ distances (including $\ell_\infty$) under a wide variety of compactly supported wavelet bases are presented in this paper. For the Haar basis, a polynomial time approximation scheme is demonstrated. These algorithms are applicable in the one-pass sublinear-space data stream model of computation. They generalize naturally to multiple dimensions and weighted norms. A universal representation that provides a provable approximation guarantee under all p-norms simultaneously; and the first approximation algorithms for bit-budget versions of the problem, known as adaptive quantization, are also presented. Further, it is shown that the algorithms presented here can be used to select a basis from a tree-structured dictionary of bases and find a B-term representation of the given function that provably approximates its best dictionary-basis representation.Comment: Added a universal representation that provides a provable approximation guarantee under all p-norms simultaneousl

Wavelet-based multiresolution data representations for scalable distributed GIS services

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2002.Includes bibliographical references (p. 155-160).Demand for providing scalable distributed GIS services has been growing greatly as the Internet continues to boom. However, currently available data representations for these services are limited by a deficiency of scalability in data formats. In this research, four types of multiresolution data representations based on wavelet theories have been put forward. The designed Wavelet Image (WImg) data format helps us to achieve dynamic zooming and panning of compressed image maps in a prototype GIS viewer. The Wavelet Digital Elevation Model (WDEM) format is developed to deal with cell-based surface data. A WDEM is better than a raster pyramid in that a WDEM provides a non-redundant multiresolution representation. The Wavelet Arc (WArc) format is developed for decomposing curves into a multiresolution format through the lifting scheme. The Wavelet Triangulated Irregular Network (WTIN) format is developed to process general terrain surfaces based on the second generation wavelet theory. By designing a strategy to resample a terrain surface at subdivision points through the modified Butterfly scheme, we achieve the result: only one wavelet coefficient needs to be stored for each point in the final representation. In contrast to this result, three wavelet coefficients need to be stored for each point in a general 3D object wavelet-based representation. Our scheme is an interpolation scheme and has much better performance than the Hat wavelet filter on a surface. Boundary filters are designed to make the representation consistent with the rectangular boundary constraint.(cont.) We use a multi-linked list and a quadtree array as the data structures for computing. A method to convert a high resolution DEM to a WTIN is also provided. These four wavelet-based representations provide consistent and efficient multiresolution formats for online GIS. This makes scalable distributed GIS services more efficient and implementable.by Jingsong Wu.Ph.D

Minimal Representation of Electrocardiogram Signals: Towards Low-Cost Telecardiology

This thesis seeks methods for minimal linear representation and subsequently low rate sampling of electrocardiogram (ECG) signals. ECG, a non-invasive approach to record heart's electrical activity, has been an ubiquitous tool for preliminary as well as complicated diagnoses of heart related issues. The modern lifestyle of ever increasing population has elevated the rate of heart diseases. Many a times, periodic monitoring of ECG, such as holter monitors, becomes imperative for diagnosis and curing of heart conditions. Some of the major issues in maintaining quality of healthcare services are low doctor to patient ratio in urban as well as resource constrained rural localities, unavailability of trained medical professionals in remote areas, infrastructural constraints etc. In this backdrop, personalized and mobile healthcare, such as telecardiology has been proposed. In order to realize a resource friendly telecardiology system, several engineering aspects need attention. This thesis focuses on a few related signal processing issues. Specifically, compact representation and low rate sampling of ECG signals, subject to certain representation/ reconstruction accuracy are discussed. It is observed that `sym4' and `db4' wavelets pack the energy of various ECG signals in least number of coeficients. Further, the proposed hybrid Fourier/ wavelet method is shown to offer even sparser representation by using Fourier approximation for the low frequency component and wavelet approximation for the remaining part of the signals. The former contains most of the signal energy whereas the latter accounts for key clinical information at feature points. Next, sparsity of ECG signals is exploited to demonstrate near universality of the proposed nonuniform sampling scheme. Recent advances in compressive sensing (CS) theory have facilitated recovery from samples acquired in a nonuniform manner. The evaluation of proposed methods is based on empirical studies on large ECG datasets available publicly. This is justified as proposing a statistical model for ECG signals is difficult on account of wide variety of such signals. Objective quality measures are used to judge the performance

Super Resolution of Wavelet-Encoded Images and Videos

In this dissertation, we address the multiframe super resolution reconstruction problem for wavelet-encoded images and videos. The goal of multiframe super resolution is to obtain one or more high resolution images by fusing a sequence of degraded or aliased low resolution images of the same scene. Since the low resolution images may be unaligned, a registration step is required before super resolution reconstruction. Therefore, we first explore in-band (i.e. in the wavelet-domain) image registration; then, investigate super resolution. Our motivation for analyzing the image registration and super resolution problems in the wavelet domain is the growing trend in wavelet-encoded imaging, and wavelet-encoding for image/video compression. Due to drawbacks of widely used discrete cosine transform in image and video compression, a considerable amount of literature is devoted to wavelet-based methods. However, since wavelets are shift-variant, existing methods cannot utilize wavelet subbands efficiently. In order to overcome this drawback, we establish and explore the direct relationship between the subbands under a translational shift, for image registration and super resolution. We then employ our devised in-band methodology, in a motion compensated video compression framework, to demonstrate the effective usage of wavelet subbands. Super resolution can also be used as a post-processing step in video compression in order to decrease the size of the video files to be compressed, with downsampling added as a pre-processing step. Therefore, we present a video compression scheme that utilizes super resolution to reconstruct the high frequency information lost during downsampling. In addition, super resolution is a crucial post-processing step for satellite imagery, due to the fact that it is hard to update imaging devices after a satellite is launched. Thus, we also demonstrate the usage of our devised methods in enhancing resolution of pansharpened multispectral images

A Framework for Vision-based Static Hand Gesture Recognition

In today’s technical world, the intellectual computing of a efficient human-computer interaction (HCI) or human alternative and augmentative communication (HAAC) is essential in our lives. Hand gesture recognition is one of the most important techniques that can be used to build up a gesture based interface system for HCI or HAAC application. Therefore, suitable development of gesture recognition method is necessary to design advance hand gesture recognition system for successful applications like robotics, assistive systems, sign language communication, virtual reality etc. However, the variation of illumination, rotation, position and size of gesture images, efficient feature representation, and classification are the main challenges towards the development of a real time gesture recognition system. The aim of this work is to develop a framework for vision based static hand gesture recognition which overcomes the challenges of illumination, rotation, size and position variation of the gesture images. In general, a framework for gesture recognition system which consists of preprocessing, feature extraction, feature selection, and classification stages is developed in this thesis work. The preprocessing stage involves the following sub-stages: image enhancement which enhances the image by compensating illumination variation; segmentation, which segments hand region from its background image and transforms it into binary silhouette; image rotation that makes the segmented gesture as rotation invariant; filtering that effectively removes background noise and object noise from binary image and provides a well defined segmented hand gesture. This work proposes an image rotation technique by coinciding the first principal component of the segmented hand gesture with vertical axes to make it as rotation invariant. In the feature extraction stage, this work extracts xi localized contour sequence (LCS) and block based features, and proposes a combined feature set by appending LCS features with block-based features to represent static hand gesture images. A discrete wavelets transform (DWT) and Fisher ratio (F-ratio) based feature set is also proposed for better representation of static hand gesture image. To extract this feature set, DWT is applied on resized and enhanced grayscale image and then the important DWT coefficient matrices are selected as features using proposed F-ratio based coefficient matrices selection technique. In sequel, a modified radial basis function neural network (RBF-NN) classifier based on k-mean and least mean square (LMS) algorithms is proposed in this work. In the proposed RBF-NN classifier, the centers are automatically selected using k-means algorithm and estimated weight matrix is updated utilizing LMS algorithm for better recognition of hand gesture images. A sigmoidal activation function based RBF-NN classifier is also proposed here for further improvement of recognition performance. The activation function of the proposed RBF-NN classifier is formed using a set of composite sigmoidal functions. Finally, the extracted features are applied as input to the classifier to recognize the class of static hand gesture images. Subsequently, a feature vector optimization technique based on genetic algorithm (GA) is also proposed to remove the redundant and irrelevant features. The proposed algorithms are tested on three static hand gesture databases which include grayscale images with uniform background (Database I and Database II) and color images with non-uniform background (Database III). Database I is a repository database which consists of hand gesture images of 25 Danish/international sign language (D/ISL) hand alphabets. Database II and III are indigenously developed using VGA Logitech Webcam (C120) with 24 American Sign Language (ASL) hand alphabets

SUBDIVIDE AND CONQUER RESOLUTION

This contribution will be freewheeling in the domain of signal, image and surface processing and touch briefly upon some topics that have been close to the heart of people in our research group. A lot of the research of the last 20 years in this domain that has been carried out world wide is dealing with multiresolution. Multiresolution allows to represent a function (in the broadest sense) at different levels of detail. This was not only applied in signals and images but also when solving all kinds of complex numerical problems. Since wavelets came into play in the 1980's, this idea was applied and generalized by many researchers. Therefore we use this as the central idea throughout this text. Wavelets, subdivision and hierarchical bases are the appropriate tools to obtain these multiresolution effects. We shall introduce some of the concepts in a rather informal way and show that the same concepts will work in one, two and three dimensions. The applications in the three cases are however quite different, and thus one wants to achieve very different goals when dealing with signals, images or surfaces. Because completeness in our treatment is impossible, we have chosen to describe two case studies after introducing some concepts in signal processing. These case studies are still the subject of current research. The first one attempts to solve a problem in image processing: how to approximate an edge in an image efficiently by subdivision. The method is based on normal offsets. The second case is the use of Powell-Sabin splines to give a smooth multiresolution representation of a surface. In this context we also illustrate the general method of construction of a spline wavelet basis using a lifting scheme

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

Biometric Systems

Biometric authentication has been widely used for access control and security systems over the past few years. The purpose of this book is to provide the readers with life cycle of different biometric authentication systems from their design and development to qualification and final application. The major systems discussed in this book include fingerprint identification, face recognition, iris segmentation and classification, signature verification and other miscellaneous systems which describe management policies of biometrics, reliability measures, pressure based typing and signature verification, bio-chemical systems and behavioral characteristics. In summary, this book provides the students and the researchers with different approaches to develop biometric authentication systems and at the same time includes state-of-the-art approaches in their design and development. The approaches have been thoroughly tested on standard databases and in real world applications

Subseries Join and Compression of Time Series Data Based on Non-uniform Segmentation

A time series is composed of a sequence of data items that are measured at uniform intervals. Many application areas generate or manipulate time series, including finance, medicine, digital audio, and motion capture. Efficiently searching a large time series database is still a challenging problem, especially when partial or subseries matches are needed. This thesis proposes a new denition of subseries join, a symmetric generalization of subseries matching, which finds similar subseries in two or more time series datasets. A solution is proposed to compute the subseries join based on a hierarchical feature representation. This hierarchical feature representation is generated by an anisotropic diffusion scale-space analysis and a non-uniform segmentation method. Each segment is represented by a minimal polynomial envelope in a reduced-dimensionality space. Based on the hierarchical feature representation, all features in a dataset are indexed in an R-tree, and candidate matching features of two datasets are found by an R-tree join operation. Given candidate matching features, a dynamic programming algorithm is developed to compute the final subseries join. To improve storage efficiency, a hierarchical compression scheme is proposed to compress features. The minimal polynomial envelope representation is transformed to a Bezier spline envelope representation. The control points of each Bezier spline are then hierarchically differenced and an arithmetic coding is used to compress these differences. To empirically evaluate their effectiveness, the proposed subseries join and compression techniques are tested on various publicly available datasets. A large motion capture database is also used to verify the techniques in a real-world application. The experiments show that the proposed subseries join technique can better tolerate noise and local scaling than previous work, and the proposed compression technique can also achieve about 85% higher compression rates than previous work with the same distortion error