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A Novel Signal Modeling Method Using the Wavelet Transform
"... This paper presents a novel methodology for improving the modeling of nonsmooth signals, based on the wavelet transform and neural network function approximation techniques. It is suggested that the enhanced time frequency localization properties of the wavelet transform could provide the means for ..."
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This paper presents a novel methodology for improving the modeling of nonsmooth signals, based on the wavelet transform and neural network function approximation techniques. It is suggested that the enhanced time frequency localization properties of the wavelet transform could provide the means
Singularity Detection And Processing With Wavelets
 IEEE Transactions on Information Theory
, 1992
"... Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavele ..."
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Cited by 590 (13 self)
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of their wavelet transform are explained. We then prove that the local maxima of a wavelet transform detect the location of irregular structures and provide numerical procedures to compute their Lipschitz exponents. The wavelet transform of singularities with fast oscillations have a different behavior that we
Factoring wavelet transforms into lifting steps
 J. Fourier Anal. Appl
, 1998
"... ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This dec ..."
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Cited by 573 (8 self)
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ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures
Shiftable Multiscale Transforms
, 1992
"... Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavel ..."
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Cited by 557 (36 self)
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Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal
A Practical Guide to Wavelet Analysis
, 1998
"... A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finitelength t ..."
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Cited by 833 (3 self)
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A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite
Image denoising using a scale mixture of Gaussians in the wavelet domain
 IEEE TRANS IMAGE PROCESSING
, 2003
"... We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vecto ..."
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Cited by 514 (17 self)
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We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian
Waveletbased statistical signal processing using hidden Markov models
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 1998
"... Waveletbased statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many realworld signals. In this paper, we develop a new framework for statistical signal processing b ..."
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Cited by 417 (55 self)
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Waveletbased statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many realworld signals. In this paper, we develop a new framework for statistical signal processing
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 496 (2 self)
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. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
A new learning algorithm for blind signal separation

, 1996
"... A new online learning algorithm which minimizes a statistical dependency among outputs is derived for blind separation of mixed signals. The dependency is measured by the average mutual information (MI) of the outputs. The source signals and the mixing matrix are unknown except for the number of ..."
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Cited by 614 (80 self)
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of the sources. The GramCharlier expansion instead of the Edgeworth expansion is used in evaluating the MI. The natural gradient approach is used to minimize the MI. A novel activation function is proposed for the online learning algorithm which has an equivariant property and is easily implemented on a neural
Results 1  10
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