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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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. 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 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. Essentially we can think of them as data building blocks. Their fundamental property is that they allow for representations which are efficient and which can be computed fast. In other words, wavelets are capable of quickly capturing the essence of a data set with only a small set of coefficients. This is based on the fact that most data sets have correlation both in time (or space) and frequenc...
Operator Theory and Harmonic Analysis
, 1996
"... Contents 1. Spectral Theory of Bounded Operators (A) Spectra and resolvents of bounded operators on Banach spaces (B) Holomorphic functional calculi of bounded operators 2. Spectral Theory of Unbounded Operators (C) Spectra and resolvents of closed operators in Banach spaces (D) Holomorphic function ..."
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Cited by 39 (11 self)
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Contents 1. Spectral Theory of Bounded Operators (A) Spectra and resolvents of bounded operators on Banach spaces (B) Holomorphic functional calculi of bounded operators 2. Spectral Theory of Unbounded Operators (C) Spectra and resolvents of closed operators in Banach spaces (D) Holomorphic functional calculi of operators of type S!+ 3. Quadratic Estimates (E) Quadratic norms of operators of type S!+ in Hilbert spaces (F) Boundedness of holomorphic functional calculi 4. Operators with Bounded Holomorphic Functional Calculi (G) Accretive operators (H) Operators of type S! and spectral projections 5. Singular Integrals (I) Convolutions and the functional calculus of \Gammai d dx (J) The Hilbert transform and Hardy spaces 6. Calder'onZygmund Theory (K) Maximal functions and the Calder'onZygmund decomposition (L) Singular integral operators 7. Functional Ca
Compactly Supported Wavelets Which Are Biorthogonal with Respect to a Weighted Inner Product
 In Proceedings of the 14th IMACS World Congress
"... this paper we show how to construct wavelets adapted to a weighted inner product. We call such wavelets weighted wavelets . ..."
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Cited by 4 (0 self)
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this paper we show how to construct wavelets adapted to a weighted inner product. We call such wavelets weighted wavelets .