Wavelet and wavelet packet compression of electrocardiograms

Wavelets on graphs via spectral graph theory

Abstract: We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian L. Given a wavelet generating kernel g and a scale parameter t, we define the scaled wavelet operator Ttg = g(tL). The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. Subject to an admissibility condition on g, this procedure defines an invertible transform. We explore the localization properties of the wavelets in the limit of fine scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing L. We highlight potential applications of the transform through examples of wavelets on graphs corresponding to a variety of different problem domains.

Wavelets on Graphs via Spectral Graph Theory

Abstract: We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian $\L$. Given a wavelet generating kernel $g$ and a scale parameter $t$, we define the scaled wavelet operator $T_g^t = g(t\L)$. The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. Subject to an admissibility condition on $g$, this procedure defines an invertible transform. We explore the localization properties of the wavelets in the limit of fine scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing $\L$. We highlight potential applications of the transform through examples of wavelets on graphs corresponding to a variety of different problem domains.

Compressed Sensing for Real-Time Energy-Efficient ECG Compression on Wireless Body Sensor Nodes

Abstract: Wireless body sensor networks (WBSN) hold the promise to be a key enabling information and communications technology for next-generation patient-centric telecardiology or mobile cardiology solutions. Through enabling continuous remote cardiac monitoring, they have the potential to achieve improved personalization and quality of care, increased ability of prevention and early diagnosis, and enhanced patient autonomy, mobility, and safety. However, state-of-the-art WBSN-enabled ECG monitors still fall short of the required functionality, miniaturization, and energy efficiency. Among others, energy efficiency can be improved through embedded ECG compression, in order to reduce airtime over energy-hungry wireless links. In this paper, we quantify the potential of the emerging compressed sensing (CS) signal acquisition/compression paradigm for low-complexity energy-efficient ECG compression on the state-of-the-art Shimmer WBSN mote. Interestingly, our results show that CS represents a competitive alternative to state-of-the-art digital wavelet transform (DWT)-based ECG compression solutions in the context of WBSN-based ECG monitoring systems. More specifically, while expectedly exhibiting inferior compression performance than its DWT-based counterpart for a given reconstructed signal quality, its substantially lower complexity and CPU execution time enables it to ultimately outperform DWT-based ECG compression in terms of overall energy efficiency. CS-based ECG compression is accordingly shown to achieve a 37.1% extension in node lifetime relative to its DWT-based counterpart for “good” reconstruction quality.

Exploiting smart e-Health gateways at the edge of healthcare Internet-of-Things

Abstract: Current developments in ICTs such as in Internet-of-Things (IoT) and CyberPhysical Systems (CPS) allow us to develop healthcare solutions with more intelligent and prediction capabilities both for daily life (home/office) and in-hospitals. In most of IoT-based healthcare systems, especially at smart homes or hospitals, a bridging point (i.e.,gateway) is needed between sensor infrastructure network and the Internet. The gateway at the edge of the network often just performs basic functions such as translating between the protocols used in the Internet and sensor networks. These gateways have beneficial knowledge and constructive control over both the sensor network and the data to be transmitted through the Internet. In this paper, we exploit the strategic position of such gateways at the edge of the network to offer several higher-level services such as local storage, real-time local data processing, embedded data mining, etc., presenting thus a Smart e-Health Gateway. We then propose to exploit the concept of Fog Computing in Healthcare IoT systems by forming a Geo-distributed intermediary layer of intelligence between sensor nodes and Cloud. By taking responsibility for handling some burdens of the sensor network and a remote healthcare center, our Fog-assisted system architecture can cope with many challenges in ubiquitous healthcare systems such as mobility, energy efficiency, scalability, and reliability issues. A successful implementation of Smart e-Health Gateways can enable massive deployment of ubiquitous health monitoring systems especially in clinical environments. We also present a prototype of a Smart e-Health Gateway called UT-GATE where some of the discussed higher-level features have been implemented. We also implement an IoT-based Early Warning Score (EWS) health monitoring to practically show the efficiency and relevance of our system on addressing a medical case study. Our proof-of-concept design demonstrates an IoT-based health monitoring system with enhanced overall system intelligence, energy efficiency, mobility, performance, interoperability, security, and reliability.

Recommendations for the Standardization and Interpretation of the Electrocardiogram

Abstract: This statement provides a concise list of diagnostic terms for ECG interpretation that can be shared by students, teachers, and readers of electrocardiography. This effort was motivated by the existence of multiple automated diagnostic code sets containing imprecise and overlapping terms. An intended outcome of this statement list is greater uniformity of ECG diagnosis and a resultant improvement in patient care. The lexicon includes primary diagnostic statements, secondary diagnostic statements, modifiers, and statements for the comparison of ECGs. This diagnostic lexicon should be reviewed and updated periodically.

A theory for multiresolution signal decomposition: the wavelet representation

Abstract: Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed. >

Ten lectures on wavelets

Abstract: Introduction Preliminaries and notation The what, why, and how of wavelets The continuous wavelet transform Discrete wavelet transforms: Frames Time-frequency density and orthonormal bases Orthonormal bases of wavelets and multiresolutional analysis Orthonormal bases of compactly supported wavelets More about the regularity of compactly supported wavelets Symmetry for compactly supported wavelet bases Characterization of functional spaces by means of wavelets Generalizations and tricks for orthonormal wavelet bases References Indexes.

Ten Lectures on Wavelets

Abstract: Introduction Preliminaries and notation The what, why, and how of wavelets The continuous wavelet transform Discrete wavelet transforms: Frames Time-frequency density and orthonormal bases Orthonormal bases of wavelets and multiresolutional analysis Orthonormal bases of compactly supported wavelets More about the regularity of compactly supported wavelets Symmetry for compactly supported wavelet bases Characterization of functional spaces by means of wavelets Generalizations and tricks for orthonormal wavelet bases References Indexes.

Orthonormal bases of compactly supported wavelets

Abstract: We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches.

A new, fast, and efficient image codec based on set partitioning in hierarchical trees

Abstract: Embedded zerotree wavelet (EZW) coding, introduced by Shapiro (see IEEE Trans. Signal Processing, vol.41, no.12, p.3445, 1993), is a very effective and computationally simple technique for image compression. We offer an alternative explanation of the principles of its operation, so that the reasons for its excellent performance can be better understood. These principles are partial ordering by magnitude with a set partitioning sorting algorithm, ordered bit plane transmission, and exploitation of self-similarity across different scales of an image wavelet transform. Moreover, we present a new and different implementation based on set partitioning in hierarchical trees (SPIHT), which provides even better performance than our previously reported extension of EZW that surpassed the performance of the original EZW. The image coding results, calculated from actual file sizes and images reconstructed by the decoding algorithm, are either comparable to or surpass previous results obtained through much more sophisticated and computationally complex methods. In addition, the new coding and decoding procedures are extremely fast, and they can be made even faster, with only small loss in performance, by omitting entropy coding of the bit stream by the arithmetic code.