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2,813
A theory for multiresolution signal decomposition : the wavelet representation
 IEEE Transaction on Pattern Analysis and Machine Intelligence
, 1989
"... AbstractMultiresolution representations are very effective for analyzing the information content of images. We study the properties of the operator which approximates a signal at a given resolution. We show that the difference of information between the approximation of a signal at the resolutions ..."
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Cited by 3538 (12 self)
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multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror lilters. For images, the wavelet representation differentiates several spatial orientations. We study the application of this representation to data compression
The Contourlet Transform: An Efficient Directional Multiresolution Image Representation
 IEEE TRANSACTIONS ON IMAGE PROCESSING
"... The limitations of commonly used separable extensions of onedimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a “true” twodimensional transform that can capture the intrinsic geometrical structure t ..."
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Cited by 513 (20 self)
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functions with discontinuities along twice continuously differentiable curves. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications.
USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
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Cited by 1399 (16 self)
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The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking
Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
 IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
, 2007
"... Many problems in signal processing and statistical inference involve finding sparse solutions to underdetermined, or illconditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined with a spa ..."
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Cited by 539 (17 self)
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of applications, often being significantly faster (in terms of computation time) than competing methods. Although the performance of GP methods tends to degrade as the regularization term is deemphasized, we show how they can be embedded in a continuation scheme to recover their efficient practical performance.
A Fluidbased Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED
 Proc. SIGCOMM 2000
, 2000
"... In this paper we use jump process driven Stochastic Differential Equations to model the interactions of a set of TCP flows and Active Queue Management routers in a network setting. We show how the SDEs can be transformed into a set of Ordinary Differential Equations which can be easily solved numeri ..."
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Cited by 417 (21 self)
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In this paper we use jump process driven Stochastic Differential Equations to model the interactions of a set of TCP flows and Active Queue Management routers in a network setting. We show how the SDEs can be transformed into a set of Ordinary Differential Equations which can be easily solved
Efficient exact stochastic simulation of chemical systems with many species and many channels
 J. Phys. Chem. A
, 2000
"... There are two fundamental ways to view coupled systems of chemical equations: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more comm ..."
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Cited by 427 (5 self)
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There are two fundamental ways to view coupled systems of chemical equations: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more
WAVELET TRANSFORM AND DIFFUSION EQUATIONS: APPLICATIONS TO THE PROCESSING OF THE “CASSINI ” SPACECRAFT OBSERVATIONS
, 2005
"... We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fastoscillation function by the solution of the diffusion differential equations. The most important advantage of this approach is that the initial data can be represented by n ..."
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We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fastoscillation function by the solution of the diffusion differential equations. The most important advantage of this approach is that the initial data can be represented
13 The Generalized CliffordHermite Continuous Wavelet Transform
"... ABSTRACT Specific wavelet kernel functions for a continuous wavelet transform in Euclidean space are constructed in the framework of Clifford analysis. Their relationship with the heat equation and a newly introduced wavelet differential equation is established. 1 ..."
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Cited by 1 (0 self)
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ABSTRACT Specific wavelet kernel functions for a continuous wavelet transform in Euclidean space are constructed in the framework of Clifford analysis. Their relationship with the heat equation and a newly introduced wavelet differential equation is established. 1
Application of the Haar wavelet transform to solving integral and differential equations
, 2007
"... ..."
Composite Wavelet Bases for Operator Equations
 MATH. COMP
, 1996
"... This paper is concerned with the construction of biorthogonal wavelet bases defined on a union of parametric images of the unit dcube. These bases are to satisfy certain requirements imposed by applications to a class of operator equations acting on such domains. This covers also elliptic boundary ..."
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Cited by 88 (21 self)
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This paper is concerned with the construction of biorthogonal wavelet bases defined on a union of parametric images of the unit dcube. These bases are to satisfy certain requirements imposed by applications to a class of operator equations acting on such domains. This covers also elliptic boundary
Results 1  10
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2,813