Wavelet sampling techniques

In this paper we present several techniques to calculate the wavelet coe cients of a function from its samples. Interpolation, quadrature formulae and ltering methods are discussed and compared.

[1]  Gilbert G. Walter,et al.  A sampling theorem for wavelet subspaces , 1992, IEEE Trans. Inf. Theory.

[2]  W. Sweldens,et al.  Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions , 1994 .

[3]  C. Chui Wavelets: A Tutorial in Theory and Applications , 1992 .

[4]  Stéphane Mallat,et al.  Multifrequency channel decompositions of images and wavelet models , 1989, IEEE Trans. Acoust. Speech Signal Process..

[5]  A. Aldroubi,et al.  Sampling procedures in function spaces and asymptotic equivalence with shannon's sampling theory , 1994 .

[6]  Mark J. Shensa,et al.  The discrete wavelet transform: wedding the a trous and Mallat algorithms , 1992, IEEE Trans. Signal Process..

[7]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[8]  G. Strang,et al.  Fourier Analysis of the Finite Element Method in Ritz-Galerkin Theory , 1969 .

[9]  A. Cohen Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 61, I. Daubechies, SIAM, 1992, xix + 357 pp. , 1994 .

[10]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[11]  Naoki Saito,et al.  Multiresolution representations using the auto-correlation functions of compactly supported wavelets , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[12]  Naoki Saito,et al.  Multiresolution representations using the autocorrelation functions of compactly supported wavelets , 1993, IEEE Trans. Signal Process..

[13]  S. Mallat Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[14]  I. Daubechies Orthonormal bases of compactly supported wavelets , 1988 .

[15]  David L. Donoho,et al.  Interpolating Wavelet Transforms , 1992 .

[16]  Gilles Deslauriers,et al.  Symmetric iterative interpolation processes , 1989 .

[17]  Gilbert Strang,et al.  Wavelets and Dilation Equations: A Brief Introduction , 1989, SIAM Rev..

[18]  I. J. Schoenberg,et al.  Cardinal interpolation and spline functions , 1969 .

[19]  I. Daubechies,et al.  Multiresolution analysis, wavelets and fast algorithms on an interval , 1993 .

[20]  A. Aldroubi,et al.  Families of wavelet transforms in connection with Shannon's sampling theory and the Gabor transform , 1993 .

[21]  I. Daubechies,et al.  Biorthogonal bases of compactly supported wavelets , 1992 .

[22]  I. G. BONNER CLAPPISON Editor , 1960, The Electric Power Engineering Handbook - Five Volume Set.

[23]  C. Chui,et al.  Wavelets on a Bounded Interval , 1992 .

[24]  D. Donoho Smooth Wavelet Decompositions with Blocky Coefficient Kernels , 1993 .

[25]  A. Janssen The Zak transform : a signal transform for sampled time-continuous signals. , 1988 .

[26]  Wim Sweldens,et al.  An Overview of Wavelet Based Multiresolution Analyses , 1994, SIAM Rev..

[27]  R. Coifman,et al.  Fast wavelet transforms and numerical algorithms I , 1991 .

[28]  Augustus J. E. M. Janssen,et al.  The Zak transform and sampling theorems for wavelet subspaces , 1993, IEEE Trans. Signal Process..

[29]  A. Aldroubi,et al.  Families of multiresolution and wavelet spaces with optimal properties , 1993 .

[30]  Y. Meyer Ondelettes sur l'intervalle. , 1991 .

[31]  L. Schumaker,et al.  Recent advances in wavelet analysis , 1995 .

[32]  I. Daubechies Orthonormal bases of compactly supported wavelets II: variations on a theme , 1993 .

[33]  C. Micchelli,et al.  Stationary Subdivision , 1991 .