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Journal ArticleDOI

Wavelet and wavelet packet compression of electrocardiograms

01 May 1997-IEEE Transactions on Biomedical Engineering (IEEE Trans Biomed Eng)-Vol. 44, Iss: 5, pp 394-402
TL;DR: Pilot data from a blind evaluation of compressed ECG's by cardiologists suggest that the clinically useful information present in original ECG signals is preserved by 8:1 compression, and in most cases 16:1 compressed ECGs are clinically useful.
Abstract: Wavelets and wavelet packets have recently emerged as powerful tools for signal compression. Wavelet and wavelet packet-based compression algorithms based on embedded zerotree wavelet (EZW) coding are developed for electrocardiogram (ECG) signals, and eight different wavelets are evaluated for their ability to compress Holter ECG data. Pilot data from a blind evaluation of compressed ECG's by cardiologists suggest that the clinically useful information present in original ECG signals is preserved by 8:1 compression, and in most cases 16:1 compressed ECG's are clinically useful.
Citations
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Journal ArticleDOI
TL;DR: A novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph using the spectral decomposition of the discrete graph Laplacian L, based on defining scaling using the graph analogue of the Fourier domain.

1,681 citations

Posted Content
TL;DR: In this paper, the spectral graph wavelet operator is defined based on spectral decomposition of the discrete graph Laplacian, and a wavelet generating kernel and a scale parameter are used to localize this operator to an indicator function.
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.

1,119 citations

Journal ArticleDOI
TL;DR: This paper proposes 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 and presents a prototype of a Smart e-Health Gateway called UT-GATE.

867 citations

Journal ArticleDOI
TL;DR: This paper quantifies 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 and shows that CS represents a competitive alternative to state- of- the-art digital wavelet transform (DWT)-basedECG compression solutions in the context of WBSn-based ECG monitoring systems.
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.

680 citations

Journal ArticleDOI
TL;DR: This statement examines the relation of the resting ECG to its technology to establish standards that will improve the accuracy and usefulness of the ECG in practice and to recommend recommendations for ECG standards.

649 citations

References
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Journal ArticleDOI
TL;DR: Two examples of jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored and the usefulness of these image representations for scale-space analysis, stereo disparity measurement, and image enhancement is demonstrated.
Abstract: One of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavelet transforms are also unstable with respect to dilations of the input signal and, in two dimensions, rotations of the input signal. The authors formalize these problems by defining a type of translation invariance called shiftability. In the spatial domain, shiftability corresponds to a lack of aliasing; thus, the conditions under which the property holds are specified by the sampling theorem. Shiftability may also be applied in the context of other domains, particularly orientation and scale. Jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored. Two examples of jointly shiftable transforms are designed and implemented: a 1-D transform that is jointly shiftable in position and scale, and a 2-D transform that is jointly shiftable in position and orientation. The usefulness of these image representations for scale-space analysis, stereo disparity measurement, and image enhancement is demonstrated. >

1,448 citations

01 Jan 2011
TL;DR: Spectral Methods in Fluid DynamicsNumerical Methods for Partial Differential Equations (PDE): Theory and Applications of Spectral Methods: Theory and ApplicatonsSpectral methods for Incompressible Viscous FlowAdvances in Numerical Analysis: Nonlinear partial differential equations and dynamical systemsSpectral method using Multivariate polynomials on the Unit Ball as discussed by the authors.
Abstract: Spectral Methods in Fluid DynamicsNumerical Methods for Partial Differential EquationsNumerical Analysis of Partial Differential EquationsNumerical analysis of spectral methods : theory and applicationsSpectral Methods And Their ApplicationsA Brief Introduction to Numerical AnalysisA First Course in the Numerical Analysis of Differential Equations South Asian EditionConvergence of Spectral Methods for Hyperbolic Initial-boundary Value SystemsReview of Some Approximation Operators for the Numerical Analysis of Spectral MethodsSpectral Methods in MATLABA Modified Spectral Method in Phase SpaceThe Birth of Numerical AnalysisSpectral Methods for Non-Standard Eigenvalue ProblemsPartial Differential EquationsNumerical Analysis of Spectral MethodsNumerical Analysis of Partial Differential Equations Using Maple and MATLABSpectral MethodsSpectral Methods for NonStandard Eigenvalue ProblemsAn Introduction to the Numerical Analysis of Spectral MethodsSpectral Methods in Time for Parabolic ProblemsSpectral Methods in Chemistry and PhysicsA First Course in the Numerical Analysis of Differential Equations South Asian EditionSummary of Research in Applied Mathematics, Numerical Analysis and Computer Science at the Institute for Computer Applications in Science and EngineeringNumerical AnalysisSpectral Methods for Compressible Flow ProblemsA First Course in the Numerical Analysis of Differential EquationsSummary of Research in Applied Mathematics, Numerical Analysis, and Computer SciencesA Theoretical Introduction to Numerical AnalysisNumerical AnalysisRiemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special FunctionsSpectral MethodsSpectral Methods for Uncertainty QuantificationSpectral Methods and Their ApplicationsNumerical Analysis of Spectral Methods: Theory and ApplicatonsSpectral Methods for Incompressible Viscous FlowAdvances in Numerical Analysis: Nonlinear partial differential equations and dynamical systemsSpectral Methods Using Multivariate Polynomials on the Unit BallA First Course in the Numerical Analysis of Differential EquationsFundamentals of Engineering Numerical AnalysisSpectral Methods for Time-Dependent Problems

1,425 citations

Journal ArticleDOI
TL;DR: In this paper, the authors discuss several constructions of orthonormal wavelet bases on the interval, and introduce a new construction that avoids some of the disadvantages of earlier constructions.

1,065 citations


"Wavelet and wavelet packet compress..." refers background in this paper

  • ...A fourth solution, put forth by Cohen, Daubechies, Jawerth, and Vial [4] and explained in some detail in [5], which avoids the problems mentioned above is to use a special set of basis functions at the edges of a signal and a conventional wavelet basis for the interior of the signal....

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  • ...Instructions for obtaining the lter coe cients for the edge lters can be found in [5]....

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Journal ArticleDOI
TL;DR: A fast rate-distortion (R-D) optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented.
Abstract: A fast rate-distortion (R-D) optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented. The scheme guarantees operation on the convex hull of the operational R-D curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity. Applications for this coding technique include R. Coefman et al.'s (Yale Univ., 1990) generalized multiresolution wavelet packet decomposition, iterative subband coders, and quadtree structures. Applications to image processing involving wavelet packets as well as discrete cosine transform (DCT) quadtrees are presented. >

798 citations


"Wavelet and wavelet packet compress..." refers background or methods in this paper

  • ...Wavelet packets have been used successfully to compress audio [14] and image data [ 33 ]....

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  • ...A variety of best basis cost functions have been proposed [ 33 ], [34]....

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Journal ArticleDOI
TL;DR: The theoretical bases behind the direct ECG data compression schemes are presented and classified into three categories: tolerance-comparison compression, DPCM, and entropy coding methods and a framework for evaluation and comparison of ECG compression schemes is presented.
Abstract: Electrocardiogram (ECG) compression techniques are compared, and a unified view of these techniques is established. ECG data compression schemes are presented in two major groups: direct data compression and transformation methods. The direct data compression techniques are ECG differential pulse code modulation (DPCM) and entropy coding, AZTEC, Turning-point, CORTES, Fan and SAPA algorithms, peak-picking, and cycle-to-cycle compression methods. The transformation methods include Fourier, Walsh, and Karhunen-Loeve transforms. The theoretical bases behind the direct ECG data compression schemes are presented and classified into three categories: tolerance-comparison compression, DPCM, and entropy coding methods. A framework for evaluation and comparison of ECG compression schemes is presented. >

690 citations