The Experts below are selected from a list of 2571 Experts worldwide ranked by ideXlab platform
Eugene B Postnikov - One of the best experts on this subject based on the ideXlab platform.
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computational implementation of the inverse continuous wavelet transform without a requirement of the Admissibility Condition
Applied Mathematics and Computation, 2016Co-Authors: Eugene B Postnikov, Elena A Lebedeva, Anastasia I LavrovaAbstract:Recently, it has been proven Lebedeva and Postnikov (2014) that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows an existence of the exact inverse transform. Here, we consider the computational possibility for the realization of this approach. We provide a modified simpler explanation of the reconstruction formula, restricted on the practical case of real valued finite (or periodic/periodized) samples and the standard (restricted) Morlet wavelet as a practically important example of an approximate wavelet. The provided examples of applications include the test function and the non-stationary electro-physical signals arising in the problem of neuroscience.
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computational implementation of the inverse continuous wavelet transform without a requirement of the Admissibility Condition
arXiv: Functional Analysis, 2015Co-Authors: Eugene B Postnikov, Elena A Lebedeva, Anastasia I LavrovaAbstract:Recently, it has been proven [R. Soc. Open Sci. 1 (2014) 140124] that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows for an existence of the exact inverse transform. Here we consider the computational possibility for the realization of this approach. We provide modified simpler explanation of the reconstruction formula, restricted on the practical case of real valued finite (or periodic/periodized) samples and the standard (restricted) Morlet wavelet as a practically important example of an approximate wavelet. The provided examples of applications includes the test function and the non-stationary electro-physical signals arising in the problem of neuroscience.
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On alternative wavelet reconstruction formula: a case study of approximate wavelets
Royal Society open science, 2014Co-Authors: Elena A Lebedeva, Eugene B PostnikovAbstract:The application of the continuous wavelet transform to study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies due to the Admissibility Condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the Admissibility Condition is violated. The case of the transform with the standard Morlet wavelet, which is an important example of such analyzing functions, is discussed.
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on alternative wavelet reconstruction formula a case study of approximate wavelets
Royal Society Open Science, 2014Co-Authors: Elena A Lebedeva, Eugene B PostnikovAbstract:The application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the Admissibility Condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the Admissibility Condition is violated. The case of the transform with the standard reduced Morlet wavelet, which is an important example of such analysing functions, is discussed.
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wavelet reconstruction formula that does not require the Admissibility Condition
2014Co-Authors: Elena A Lebedeva, Eugene B PostnikovAbstract:The application of the continuous wavelet transform to study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies due to the Admissibility Condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the Admissibility Condition is violated. The case of the transform with the standard Morlet wavelet, which is an important example of such analyzing functions, is discussed.
Elena A Lebedeva - One of the best experts on this subject based on the ideXlab platform.
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computational implementation of the inverse continuous wavelet transform without a requirement of the Admissibility Condition
Applied Mathematics and Computation, 2016Co-Authors: Eugene B Postnikov, Elena A Lebedeva, Anastasia I LavrovaAbstract:Recently, it has been proven Lebedeva and Postnikov (2014) that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows an existence of the exact inverse transform. Here, we consider the computational possibility for the realization of this approach. We provide a modified simpler explanation of the reconstruction formula, restricted on the practical case of real valued finite (or periodic/periodized) samples and the standard (restricted) Morlet wavelet as a practically important example of an approximate wavelet. The provided examples of applications include the test function and the non-stationary electro-physical signals arising in the problem of neuroscience.
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computational implementation of the inverse continuous wavelet transform without a requirement of the Admissibility Condition
arXiv: Functional Analysis, 2015Co-Authors: Eugene B Postnikov, Elena A Lebedeva, Anastasia I LavrovaAbstract:Recently, it has been proven [R. Soc. Open Sci. 1 (2014) 140124] that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows for an existence of the exact inverse transform. Here we consider the computational possibility for the realization of this approach. We provide modified simpler explanation of the reconstruction formula, restricted on the practical case of real valued finite (or periodic/periodized) samples and the standard (restricted) Morlet wavelet as a practically important example of an approximate wavelet. The provided examples of applications includes the test function and the non-stationary electro-physical signals arising in the problem of neuroscience.
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On alternative wavelet reconstruction formula: a case study of approximate wavelets
Royal Society open science, 2014Co-Authors: Elena A Lebedeva, Eugene B PostnikovAbstract:The application of the continuous wavelet transform to study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies due to the Admissibility Condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the Admissibility Condition is violated. The case of the transform with the standard Morlet wavelet, which is an important example of such analyzing functions, is discussed.
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on alternative wavelet reconstruction formula a case study of approximate wavelets
Royal Society Open Science, 2014Co-Authors: Elena A Lebedeva, Eugene B PostnikovAbstract:The application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the Admissibility Condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the Admissibility Condition is violated. The case of the transform with the standard reduced Morlet wavelet, which is an important example of such analysing functions, is discussed.
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wavelet reconstruction formula that does not require the Admissibility Condition
2014Co-Authors: Elena A Lebedeva, Eugene B PostnikovAbstract:The application of the continuous wavelet transform to study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies due to the Admissibility Condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the Admissibility Condition is violated. The case of the transform with the standard Morlet wavelet, which is an important example of such analyzing functions, is discussed.
Rémi Gribonval - One of the best experts on this subject based on the ideXlab platform.
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Wavelets on graphs via spectral graph theory
Applied and Computational Harmonic Analysis, 2011Co-Authors: David K. Hammond, Pierre Vandergheynst, Rémi GribonvalAbstract: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 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 Ttg = g(tL). 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.
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Wavelets on Graphs via Spectral Graph Theory
arXiv: Functional Analysis, 2009Co-Authors: David K. Hammond, Pierre Vandergheynst, Rémi GribonvalAbstract: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.
Roy Nicholas - One of the best experts on this subject based on the ideXlab platform.
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Admissible Abstractions for Near-optimal Task and Motion Planning
'International Joint Conferences on Artificial Intelligence', 2019Co-Authors: Vega-brown, William R, Roy NicholasAbstract:We define an Admissibility Condition for abstractions expressed using angelic semantics and show that these Conditions allow us to accelerate planning while preserving the ability to find the optimal motion plan. We then derive admissible abstractions for two motion planning domains with continuous state. We extract upper and lower bounds on the cost of concrete motion plans using local metric and topological properties of the problem domain. These bounds guide the search for a plan while maintaining performance guarantees. We show that abstraction can dramatically reduce the complexity of search relative to a direct motion planner. Using our abstractions, we find near-optimal motion plans in planning problems involving 1013 states without using a separate task planner
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Admissible Abstractions for Near-optimal Task and Motion Planning
2018Co-Authors: Vega-brown William, Roy NicholasAbstract:We define an Admissibility Condition for abstractions expressed using angelic semantics and show that these Conditions allow us to accelerate planning while preserving the ability to find the optimal motion plan. We then derive admissible abstractions for two motion planning domains with continuous state. We extract upper and lower bounds on the cost of concrete motion plans using local metric and topological properties of the problem domain. These bounds guide the search for a plan while maintaining performance guarantees. We show that abstraction can dramatically reduce the complexity of search relative to a direct motion planner. Using our abstractions, we find near-optimal motion plans in planning problems involving $10^{13}$ states without using a separate task planner.Comment: This document is an extended version of a paper to appear in the "27th International Joint Conference on Artificial Intelligence" in July 201
Noboru Murata - One of the best experts on this subject based on the ideXlab platform.
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Neural network with unbounded activation functions is universal approximator
Applied and Computational Harmonic Analysis, 2017Co-Authors: Sho Sonoda, Noboru MurataAbstract:Abstract This paper presents an investigation of the approximation property of neural networks with unbounded activation functions, such as the rectified linear unit (ReLU), which is the new de-facto standard of deep learning. The ReLU network can be analyzed by the ridgelet transform with respect to Lizorkin distributions. By showing three reconstruction formulas by using the Fourier slice theorem, the Radon transform, and Parseval's relation, it is shown that a neural network with unbounded activation functions still satisfies the universal approximation property. As an additional consequence, the ridgelet transform, or the backprojection filter in the Radon domain, is what the network learns after backpropagation. Subject to a constructive Admissibility Condition, the trained network can be obtained by simply discretizing the ridgelet transform, without backpropagation. Numerical examples not only support the consistency of the Admissibility Condition but also imply that some non-admissible cases result in low-pass filtering.