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116
LongTerm Forecasting of Internet Backbone Traffic: Observations and Initial Models
 In IEEE INFOCOM
, 2003
"... We introduce a methodology to predict when and where link additions/upgrades have to take place in an IP backbone network. Using SNMP statistics, collected continuously since 1999, we compute aggregate demand between any two adjacent PoPs and look at its evolution at time scales larger than one hour ..."
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Cited by 53 (3 self)
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We introduce a methodology to predict when and where link additions/upgrades have to take place in an IP backbone network. Using SNMP statistics, collected continuously since 1999, we compute aggregate demand between any two adjacent PoPs and look at its evolution at time scales larger than one hour. We show that IP backbone traffic exhibits visible long term trends, strong periodicities, and variability at multiple time scales.
NONSUBSAMPLED CONTOURLET TRANSFORM: FILTER DESIGN AND APPLICATIONS IN DENOISING
"... In this paper we study the nonsubsampled contourlet transform. We address the corresponding filter design problem using the McClellan transformation. We show how zeroes can be imposed in the filters so that the iterated structure produces regular basis functions. The proposed design framework yields ..."
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Cited by 53 (4 self)
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In this paper we study the nonsubsampled contourlet transform. We address the corresponding filter design problem using the McClellan transformation. We show how zeroes can be imposed in the filters so that the iterated structure produces regular basis functions. The proposed design framework yields filters that can be implemented efficiently through a lifting factorization. We apply the constructed transform in image noise removal where the results obtained are comparable to the stateofthe art, being superior in some cases.
Multiresolution representations using the autocorrelation functions of compactly supported wavelets
 IEEE Trans. Signal Processing
, 1993
"... CT 06520 0 ..."
Time Invariant Orthonormal Wavelet Representations
"... A simple construction of an orthonormal basis starting with a so called mother wavelet, together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications. An orthonormal basis may not, however, always be a suitable ..."
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Cited by 48 (6 self)
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A simple construction of an orthonormal basis starting with a so called mother wavelet, together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications. An orthonormal basis may not, however, always be a suitable representation of a signal, particularly when time (or space) invariance is a required property. The conventional way around this problem is to use a redundant decomposition. In this paper, we address the time invariance problem for orthonormal wavelet transforms and propose an extension to wavelet packet decompositions. We show that it is possible to achieve time invariance and preserve the orthonormality. We subsequently propose an efficient approach to obtain such a decomposition. We demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation.
Multiresolution Support Applied to Image Filtering and Restoration
, 1995
"... The notion of a multiresolution support is introduced. This is a sequence of boolean images, related to significant pixels at each of a number of resolution levels. The multiresolution support is then used for noise suppression, in the context of image filtering, or iterative image restoration. A ..."
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Cited by 39 (21 self)
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The notion of a multiresolution support is introduced. This is a sequence of boolean images, related to significant pixels at each of a number of resolution levels. The multiresolution support is then used for noise suppression, in the context of image filtering, or iterative image restoration. Algorithmic details, and a range of practical examples, illustrate this approach.
Nonlinear processing of a shift invariant DWT for noise reduction
, 1995
"... A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in some wavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of the usual orthogonal one. Another difference is the shift invariance as opposed to the traditio ..."
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Cited by 38 (8 self)
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A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in some wavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of the usual orthogonal one. Another difference is the shift invariance as opposed to the traditional orthogonal wavelet transform. We show that this new approach can be interpreted as a repeated application of Donoho's original method. The main feature is, however, a dramatically improved noise reduction compared to Donoho's approach, both in terms of the l 2 error and visually, for a large class of signals. This is shown by theoretical and experimental results, including synthetic aperture radar (SAR) images.
Scalespace derived from Bsplines
 IEEE Trans. Pattern Anal. Machine Intell
, 1998
"... Abstract—It is wellknown that the linear scalespace theory in computer vision is mainly based on the Gaussian kernel. The purpose of the paper is to propose a scalespace theory based on Bspline kernels. Our aim is twofold. On one hand, we present a general framework and show how Bsplines provid ..."
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Cited by 23 (8 self)
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Abstract—It is wellknown that the linear scalespace theory in computer vision is mainly based on the Gaussian kernel. The purpose of the paper is to propose a scalespace theory based on Bspline kernels. Our aim is twofold. On one hand, we present a general framework and show how Bsplines provide a flexible tool to design various scalespace representations: continuous scalespace, dyadic scalespace frame, and compact scalespace representation. In particular, we focus on the design of continuous scalespace and dyadic scalespace frame representation. A general algorithm is presented for fast implementation of continuous scalespace at rational scales. In the dyadic case, efficient frame algorithms are derived using Bspline techniques to analyze the geometry of an image. Moreover, the image can be synthesized from its multiscale local partial derivatives. Also, the relationship between several scalespace approaches is explored. In particular, the evolution of wavelet theory from traditional scalespace filtering can be well understood in terms of Bsplines. On the other hand, the behavior of edge models, the properties of completeness, causality, and other properties in such a scalespace representation are examined in the framework of Bsplines. It is shown that, besides the good properties inherited from the Gaussian kernel, the Bspline derived scalespace exhibits many advantages for modeling visual mechanism with regard to the efficiency, compactness, orientation feature, and parallel structure. Index Terms—Image modeling, Bspline, wavelet, scalespace, scaling theorem, fingerprint theorem.
The undecimated wavelet decomposition and its reconstruction
 IEEE Transactions on Image Processing
, 2007
"... This paper describes the undecimated wavelet transform and its reconstruction. In the first part, we show the relation between two well known undecimated wavelet transforms, the standard undecimated wavelet transform and the isotropic undecimated wavelet transform. Then we present new filter banks s ..."
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Cited by 22 (10 self)
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This paper describes the undecimated wavelet transform and its reconstruction. In the first part, we show the relation between two well known undecimated wavelet transforms, the standard undecimated wavelet transform and the isotropic undecimated wavelet transform. Then we present new filter banks specially designed for undecimated wavelet decompositions which have some useful properties such as being robust to ringing artifacts which appear generally in waveletbased denoising methods. A range of examples illustrates the results.
Combining Neural Network Forecasts on WaveletTransformed Time Series
, 1997
"... We discuss a simple strategy aimed at improving neural network prediction accuracy, based on the combination of predictions at varying resolution levels of the domain under investigation (here: time series). First, a wavelet transform is used to decompose the time series into varying scales of tempo ..."
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Cited by 20 (5 self)
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We discuss a simple strategy aimed at improving neural network prediction accuracy, based on the combination of predictions at varying resolution levels of the domain under investigation (here: time series). First, a wavelet transform is used to decompose the time series into varying scales of temporal resolution. The latter provide a sensible decomposition of the data so that the underlying temporal structures of the original time series become more tractable. Then, a Dynamical Recurrent Neural Network (DRNN) is trained on each resolution scale with the temporalrecurrent backpropagation (TRBP) algorithm. By virtue of its internal dynamic, this general class of dynamic connectionist network approximates the underlying law governing each resolution level by a system of nonlinear difference equations. The individual wavelet scale forecasts are afterwards recombined to form the current estimate. The predictive ability of this strategy is assessed with the sunspot series. Keywords  Dyna...
The redundant discrete wavelet transform and additive noise
 IEEE Signal Processing Letters
, 2005
"... Abstract — The behavior under additive noise of the redundant discrete wavelet transform (RDWT), a frame expansion that is essentially an undecimated discrete wavelet transform, is studied. Known prior results in the form of inequalities bound distortion energy in the original signal domain from add ..."
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Cited by 20 (2 self)
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Abstract — The behavior under additive noise of the redundant discrete wavelet transform (RDWT), a frame expansion that is essentially an undecimated discrete wavelet transform, is studied. Known prior results in the form of inequalities bound distortion energy in the original signal domain from additive noise in frameexpansion coefficients. In this paper, a precise relationship between RDWTdomain and originalsignaldomain distortion for additive white noise in the RDWT domain is derived. Index Terms — redundant wavelet transform, frame expansion, additive noise I.