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504,427
Approximation Algorithms for Wavelet Transform Coding of Data Streams
, 2008
"... This paper addresses the problem of finding a fterm wavelet representation of a given discrete function � P ‚ � whose distance from � is minimized. The problem is well understood when we seek to minimize the Euclidean distance between � and its representation. The firstknown algorithms for findi ..."
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pass sublinearspace data stream model of computation. They generalize naturally to multiple dimensions and weighted norms. A universal representation that provides a provable approximation guarantee under all �norms simultaneously; and the first approximation algorithms for bitbudget versions of the problem
Approximation Algorithms for Wavelet Transform Coding of Data Streams
, 2006
"... This paper addresses the problem of finding a Bterm wavelet representation of a given discrete function f ∈ R n whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance between f and its representation. The first known algorithms for finding ..."
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Cited by 24 (8 self)
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space data stream model of computation. They generalize naturally to multiple dimensions, weighted norms. The first approximation algorithms for bitbudget versions of the problem known as adaptive quantization are also given. Further, the algorithms presented here can be used to select a basis from a
Models and issues in data stream systems
 IN PODS
, 2002
"... In this overview paper we motivate the need for and research issues arising from a new model of data processing. In this model, data does not take the form of persistent relations, but rather arrives in multiple, continuous, rapid, timevarying data streams. In addition to reviewing past work releva ..."
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Cited by 770 (19 self)
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relevant to data stream systems and current projects in the area, the paper explores topics in stream query languages, new requirements and challenges in query processing, and algorithmic issues.
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
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 3460 (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
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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study separately. We show that the size of the oscillations can be measured from the wavelet transform local maxima. It has been shown that one and twodimensional signals can be reconstructed from the local maxima of their wavelet transform [14]. As an application, we develop an algorithm that removes
The Lifting Scheme: A Construction Of Second Generation Wavelets
, 1997
"... . We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to ..."
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Cited by 541 (16 self)
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to a faster, inplace calculation of the wavelet transform. Several examples are included. Key words. wavelet, multiresolution, second generation wavelet, lifting scheme AMS subject classifications. 42C15 1. Introduction. Wavelets form a versatile tool for representing general functions or data sets
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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number of ideas and approaches to approximate processing as currently being formulated in the computer science community. We then present four examples of signal processing algorithms/systems that are structured with these goals in mind. These examples may be viewed as partial inroads toward the ultimate
Approximate Frequency Counts over Data Streams
 VLDB
, 2002
"... We present algorithms for computing frequency counts exceeding a userspecified threshold over data streams. Our algorithms are simple and have provably small memory footprints. Although the output is approximate, the error is guaranteed not to exceed a userspecified parameter. Our algorithms can e ..."
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Cited by 405 (1 self)
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We present algorithms for computing frequency counts exceeding a userspecified threshold over data streams. Our algorithms are simple and have provably small memory footprints. Although the output is approximate, the error is guaranteed not to exceed a userspecified parameter. Our algorithms can
Results 1  10
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