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Proceedings of the IEEE

Issue 4 • Date Apr 1996

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Displaying Results 1 - 12 of 12
  • A review of wavelets in biomedical applications

    Page(s): 626 - 638
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    We present an overview of the various uses of the wavelet transform (WT) in medicine and biology. We start by describing the wavelet properties that are the most important for biomedical applications. In particular we provide an interpretation of the the continuous wavelet transform (CWT) as a prewhitening multiscale matched filter. We also briefly indicate the analogy between the WT and some of the the biological processing that occurs in the early components of the auditory and visual system. We then review the uses of the WT for the analysis of 1-D physiological signals obtained by phonocardiography, electrocardiography (ECG), mid electroencephalography (EEG), including evoked response potentials. Next, we provide a survey of wavelet developments in medical imaging. These include biomedical image processing algorithms (e.g., noise reduction, image enhancement, and detection of microcalcifications in mammograms), image reconstruction and acquisition schemes (tomography, and magnetic resonance imaging (MRI)), and multiresolution methods for the registration and statistical analysis of functional images of the brain (positron emission tomography (PET) and functional MRI (fMRI)). In each case, we provide the reader with same general background information and a brief explanation of how the methods work View full abstract»

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  • Wavelets and turbulence

    Page(s): 639 - 669
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    We have used wavelet transform techniques to analyze, model, and compute turbulent flows. The theory and open questions encountered in turbulence are presented. The wavelet-based techniques that we have applied to turbulence problems are explained and the main results obtained are summarized View full abstract»

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  • Wavelets and the study of the distant Universe

    Page(s): 670 - 679
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    The large-scale distribution of galaxies in the Universe exhibits structures at various scales, these so-called groups, clusters, and superclusters of galaxies being more or less hierarchically organized. A specific vision model is needed in order to detect, describe, and classify each component of this hierarchy. To do so, we have developed a multiscale vision model based on an unfolding into a scale space allowing us to detect structures of different sizes. A discrete wavelet transform is done by the a trous algorithm. The algorithm is implemented for astronomical images and also for lists of object positions, currently called catalogues in astronomical literature. Some applications on astrophysical data of cosmological interest are briefly described: (1) inventory procedures for galaxy counts on wide-field images, (2) processing of X-ray cluster images lending to the analyses of the total matter distribution, and (3) detection of large-scale structures from galaxy counts, From the analyses of N-body simulations we show that the vision model from the wavelet transform provides a new statistical indicator on cosmological scenarios View full abstract»

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  • Wavelets, subband coding, and best bases

    Page(s): 541 - 560
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    The emergence of wavelets has led to a convergence of linear expansion methods used in signal processing and applied mathematics. In particular, subband coding methods and their associated filters are closely related to wavelet constructions. We first review such constructions with a signal processing perspective. We then discuss the idea behind signal adapted bases and associated algorithms before showing how wavelets and subband coding methods are used in signal compression applications View full abstract»

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  • Wavelets for a vision

    Page(s): 604 - 614
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    Early on, computer vision researchers have realized that multiscale transforms are important to analyze the information content of images. The wavelet theory gives a stable mathematical foundation to understand the properties of such multiscale algorithms. This tutorial describes major applications to multiresolution search, multiscale edge detection, and texture discrimination View full abstract»

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  • Wavelets in computer graphics

    Page(s): 615 - 625
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    One of the perennial goals in computer graphics (CC) is realism in real time. Handling geometrically complex scenes and physically faithful descriptions of their appearance and behavior clashes with the requirement of multiple frame per second update rates. It is no surprise then that hierarchical modeling and simulation have already enjoyed a long history in CG. Most recently these ideas have received a significant boost as wavelet based algorithms have entered many areas in CG. We give an overview of some of the areas in which wavelets have already had an impact on the state of the art View full abstract»

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  • Wavelets: the mathematical background

    Page(s): 514 - 522
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    The authors give an overview of the continuous and oversampled wavelet transform. They discuss how, by sampling the continuous wavelet transform, orthonormal wavelet bases can be obtained. Multiresolution analysis, as a framework for studying wavelet bases, is also presented. Finally, the authors deal with discrete-time wavelet representations, filter banks, and fast algorithms View full abstract»

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  • Wavelets: What next?

    Page(s): 680 - 685
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    The author looks ahead to see what the future can bring to wavelet research. He tries to find a common denominator for “wavelets” and identifies promising research directions and challenging problems View full abstract»

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  • Where do wavelets come from? A personal point of view

    Page(s): 510 - 513
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    The development of wavelets is an example where ideas from many different fields combined to merge into a whole that is more than the sum of its parts. The subject area of wavelets, developed mostly over the last 15 years, is connected to older ideas in many other fields, including pure and applied mathematics, physics, computer science, and engineering. The history of wavelets can therefore be represented as a tree with roots reaching deeply and in many directions. In this picture, the trunk would correspond to the rapid development of “wavelet tools” in the second half of the 1980's, with shared efforts by researchers from many different fields; the crown of the tree, with its many branches, would correspond to different directions and applications in which wavelets are now becoming a standard part of the mathematical tool kit, alongside other more established techniques. The author gives here a highly personal version of the development of wavelets View full abstract»

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  • Wavelets and time-frequency analysis

    Page(s): 523 - 540
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    We present a selective overview of time-frequency analysis and some of its key problems. In particular we motivate the introduction of wavelet and wavelet packet analysis. Different types of decompositions of an idealized time-frequency plane provide the basis for understanding the performance of the numerical algorithms and their corresponding interpretations within the continuous models. As examples we show how to control the frequency spreading of wavelet packets at high frequencies using nonstationary filtering and study some properties of periodic wavelet packets. Furthermore we derive a formula to compute the time localization of a wavelet packet from its indexes which is exact for linear phase filters, and show how this estimate deteriorates with deviation from linear phase View full abstract»

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  • Emerging applications of multirate signal processing and wavelets in digital communications

    Page(s): 586 - 603
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    Multirate systems and filter banks have traditionally played an important role in source coding and compression for contemporary communication applications, and many of the key design issues in such applications have been extensively explored. We review developments on the comparatively less explored role of multirate filter banks and wavelets in channel coding and modulation for some important classes of channels. Some representative examples of emerging potential applications are described. One involves the use of highly dispersive, broadband multirate systems for wireless multiuser communication (spread spectrum CDMA) in the presence of fading due to time-varying multipath. Another is the wavelet-based diversity strategy referred to as “fractal modulation” for use with unpredictable communication links and in broadcast applications with user-selectable quality of service. A final example involves multitone (multicarrier) modulation systems based on multirate filter banks and fast lapped transforms for use on channels subject to severe intersymbol and narrowband interference. Collectively, these constitute intriguing, interrelated paradigms within an increasingly broad and active area of research View full abstract»

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  • Characterization of acoustic signals through continuous linear time-frequency representations

    Page(s): 561 - 585
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    One important field in the framework of computer music concerns the modeling of sounds. In order to design digital models mirroring as closely as possible a real sound and permitting in addition intimate transformations by altering the synthesis parameters, we look for a signal model based on additive synthesis whose parameters are estimated by the analysis of real sounds. This model is relevant from both the physical and perceptual points of view, especially when the sound to be analyzed comes from a musical instrument. We present some techniques, mostly unpublished, based on time-frequency representations which make possible the estimation of relevant parameters such as frequency and amplitude modulation laws corresponding to each spectral component of the sound. The techniques described extend the results presented by Delprat et al. (see IEEE Trans. Inform. Theory, vol.38, p.644-65, March 1992). These methods are then transposed to broadband signals, allowing the characterization of transients View full abstract»

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H. Joel Trussell
North Carolina State University