The Experts below are selected from a list of 8343 Experts worldwide ranked by ideXlab platform
H. Longbotham - One of the best experts on this subject based on the ideXlab platform.
-
A class of robust nonlinear filters for signal decomposition and filtering, utilizing the Haar Basis
[Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics Speech and Signal Processing, 1992Co-Authors: H. LongbothamAbstract:A class of robust nonlinear filters for signal decomposition and filtering based on the Haar Basis is discussed. The nonlinear filters with window width 2N+1 are shown to be linear over the PICO(N+1) signals (piecewise constant signals) where the minimum width of a constant region is N+1. Next, passband filtering of PICO signals, edge enhancement, and an optimality criterion for filtering of PICO signals is discussed. An application of the filters to biological data (non-PICO) is then demonstrated.
-
ICASSP - A class of robust nonlinear filters for signal decomposition and filtering, utilizing the Haar Basis
[Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics Speech and Signal Processing, 1992Co-Authors: H. LongbothamAbstract:A class of robust nonlinear filters for signal decomposition and filtering based on the Haar Basis is discussed. The nonlinear filters with window width 2N+1 are shown to be linear over the PICO(N+1) signals (piecewise constant signals) where the minimum width of a constant region is N+1. Next, passband filtering of PICO signals, edge enhancement, and an optimality criterion for filtering of PICO signals is discussed. An application of the filters to biological data (non-PICO) is then demonstrated. >
Daniel Urieli - One of the best experts on this subject based on the ideXlab platform.
-
ESA - Inner-product based wavelet synopses for range-sum queries
Lecture Notes in Computer Science, 2006Co-Authors: Yossi Matias, Daniel UrieliAbstract:In recent years wavelet based synopses were shown to be effective for approximate queries in database systems. The simplest wavelet synopses are constructed by computing the Haar transform over a vector consisting of either the raw-data or the prefix-sums of the data, and using a greedy-euristic to select the wavelet coefficients that are kept in the synopsis. The greedy-heuristic is known to be optimal for point queries w.r.t. the mean-squared-error, but no similar efficient optimality result was known for range-sum queries, for which the effectiveness of such synopses was only shown experimentally. We construct an operator that defines a norm that is equivalent to the mean-squared error over all possible range-sum queries, where the norm is measured on the prefix-sums vector. We show that the Haar Basis (and in fact any wavelet Basis) is orthogonal w.r.t. the inner product defined by this novel operator. This allows us to use Parseval-based thresholding, and thus obtain the first linear time construction of a provably optimal wavelet synopsis for range-sum queries. We show that the new thresholding is very similar to the greedy-heuristic that is based on point queries. For the case of range-sum queries over the raw data, we define a similar operator, and show that Haar Basis is not orthogonal w.r.t. the inner product defined by this operator.
-
On the Optimality of the Greedy Heuristic in Wavelet Synopses for Range Queries
2005Co-Authors: Yossi Matias, Daniel UrieliAbstract:In recent years wavelet based synopses were shown to be efiective for approximate queries in database systems. The simplest wavelet synopses are constructed by computing the Haar transform over a vector consisting of either the raw-data or the preflx-sums of the data, and using a greedy-heuristic to select the wavelet coe‐cients that are kept in the synopsis. The greedy-heuristic is known to be optimal for point queries w.r.t. the mean-squared-error, but no similar optimality result was known for range-sum queries, for which the efiectiveness of such synopses was only shown experimentally. The optimality of the greedy-heuristic for the case of point queries is due to the Haar Basis being orthonormal for this case, which allows using the Parseval-based thresholding. Thus, the main technical question we are concerned with in this paper is whether the Haar Basis is orthonormal for the case of range-sum queries. We show that it is not orthogonal for the case of range-sum queries over the raw data, and that it is orthonormal for the case of preflx-sums. Consequently, we show that a slight variation of the greedy-heuristic over the preflx-sums of the data is an optimal thresholding w.r.t. the mean-squared-error. As a result, we obtain the flrst linear time construction of a provably optimal wavelet synopsis for range-sum queries. The crux of our proof is based on a novel construction of inner products, that deflne the error measured over range-sum queries.
Denka Kutzarova - One of the best experts on this subject based on the ideXlab platform.
-
on the boundedness of threshold operators in l_1 0 1 with respect to the Haar Basis
Positivity, 2017Co-Authors: S J Dilworth, S. Gogyan, Denka Kutzarova, Th. SchlumprechtAbstract:We prove a near-unconditionality property for the normalized Haar Basis of $$L_1[0,1]$$ .
-
On the boundedness of threshold operators in $$L_1[0,1]$$ with respect to the Haar Basis
Positivity, 2016Co-Authors: Stephen J. Dilworth, S. Gogyan, Denka Kutzarova, Th. SchlumprechtAbstract:We prove a near-unconditionality property for the normalized Haar Basis of $$L_1[0,1]$$ .
-
On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis
Constructive Approximation, 2014Co-Authors: S J Dilworth, S. Gogyan, Denka KutzarovaAbstract:We define a family of weak thresholding greedy algorithms for the multivariate Haar Basis for L _1[0,1]^ d ( d ≥1). We prove convergence and uniform boundedness of the weak greedy approximants for all f ∈ L _1[0,1]^ d .
-
On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis
arXiv: Functional Analysis, 2012Co-Authors: Stephen J. Dilworth, S. Gogyan, Denka KutzarovaAbstract:We define a family of weak thresholding greedy algorithms for the multivariate Haar Basis for $L_1[0,1]^d$ ($d \ge 1$). We prove convergence and uniform boundedness of the weak greedy approximants for all $f \in L_1[0,1]^d$.
Yossi Matias - One of the best experts on this subject based on the ideXlab platform.
-
ESA - Inner-product based wavelet synopses for range-sum queries
Lecture Notes in Computer Science, 2006Co-Authors: Yossi Matias, Daniel UrieliAbstract:In recent years wavelet based synopses were shown to be effective for approximate queries in database systems. The simplest wavelet synopses are constructed by computing the Haar transform over a vector consisting of either the raw-data or the prefix-sums of the data, and using a greedy-euristic to select the wavelet coefficients that are kept in the synopsis. The greedy-heuristic is known to be optimal for point queries w.r.t. the mean-squared-error, but no similar efficient optimality result was known for range-sum queries, for which the effectiveness of such synopses was only shown experimentally. We construct an operator that defines a norm that is equivalent to the mean-squared error over all possible range-sum queries, where the norm is measured on the prefix-sums vector. We show that the Haar Basis (and in fact any wavelet Basis) is orthogonal w.r.t. the inner product defined by this novel operator. This allows us to use Parseval-based thresholding, and thus obtain the first linear time construction of a provably optimal wavelet synopsis for range-sum queries. We show that the new thresholding is very similar to the greedy-heuristic that is based on point queries. For the case of range-sum queries over the raw data, we define a similar operator, and show that Haar Basis is not orthogonal w.r.t. the inner product defined by this operator.
-
On the Optimality of the Greedy Heuristic in Wavelet Synopses for Range Queries
2005Co-Authors: Yossi Matias, Daniel UrieliAbstract:In recent years wavelet based synopses were shown to be efiective for approximate queries in database systems. The simplest wavelet synopses are constructed by computing the Haar transform over a vector consisting of either the raw-data or the preflx-sums of the data, and using a greedy-heuristic to select the wavelet coe‐cients that are kept in the synopsis. The greedy-heuristic is known to be optimal for point queries w.r.t. the mean-squared-error, but no similar optimality result was known for range-sum queries, for which the efiectiveness of such synopses was only shown experimentally. The optimality of the greedy-heuristic for the case of point queries is due to the Haar Basis being orthonormal for this case, which allows using the Parseval-based thresholding. Thus, the main technical question we are concerned with in this paper is whether the Haar Basis is orthonormal for the case of range-sum queries. We show that it is not orthogonal for the case of range-sum queries over the raw data, and that it is orthonormal for the case of preflx-sums. Consequently, we show that a slight variation of the greedy-heuristic over the preflx-sums of the data is an optimal thresholding w.r.t. the mean-squared-error. As a result, we obtain the flrst linear time construction of a provably optimal wavelet synopsis for range-sum queries. The crux of our proof is based on a novel construction of inner products, that deflne the error measured over range-sum queries.
Julien Hamonier - One of the best experts on this subject based on the ideXlab platform.
-
Wavelet series representation for multifractional multistable Riemann-Liouville process
arXiv: Probability, 2020Co-Authors: Antoine Ayache, Julien HamonierAbstract:The main goal of this paper is to construct a wavelet-type random series representation for a random field $X$, defined by a multistable stochastic integral, which generates a multifractional multistable Riemann-Liouville (mmRL) process $Y$. Such a representation provides, among other things, an efficient method of simulation of paths of $Y$. In order to obtain it, we expand in the Haar Basis the integrand associated with $X$ and we use some fundamental properties of multistable stochastic integrals. Then, thanks to the Abel's summation rule and the Doob's maximal inequality for discrete submartingales, we show that this wavelet-type random series representation of $X$ is convergent in a strong sense: almost surely in some spaces of continuous functions. Also, we determine an estimate of its almost sure rate of convergence in these spaces.
-
Linear Multifractional Stable Motion: Representation via Haar Basis
Stochastic Processes and their Applications, 2015Co-Authors: Julien HamonierAbstract:The goal of this paper is to provide a wavelet series representation for Linear Multifractional Stable Motion (LMSM). Instead of using Daubechies wavelets, which are not given in closed form, we use a Haar wavelet, thus yielding a more explicit expression than that in Ayache and Hamonier (in press).
-
Linear Multifractional Stable Motion: representation via Haar Basis
arXiv: Probability, 2014Co-Authors: Julien HamonierAbstract:The aim of this paper is to give a wavelet series representation of Linear Multifractional Stable Motion (LMSM in brief), which is more explicit than that introduced in (Ayache & Hamonier 2012). Instead of using Daubechies wavelet, which is not given by a closed form, we use the Haar wavelet. In order to obtain this new representation, we introduce a Haar expansion of the high and low frequency parts of the $\mathcal{S}\alpha \mathcal{S}$ random field $X$ generating LMSM. Then, by using Abel transforms, we show that these series are convergent, almost surely, in the space of continuous functions. Finally, we determine their almost sure rates of convergence in the latter space. Note that these representations of the high and low frequency parts of $X$, provide a new method for simulating the high and low frequency parts of LMSM.
