Abstract
We present a method for signal reconstruction based upon the location of its singularities which are identified by a wavelet transform technique. The reconstructed signal is an infconvolution spline approximant. The data for the interpolation problem which we solve comes from a compact signal coding procedure. Error bounds and convergence results for the calculated signal are given.
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References
J.M. Combes, A. Grossmann and Ph. Tchamitchian (eds.),Wavelets: Time-Frequency Methods and Phase Space (Springer, 1989).
A. Grossmann, H. Holschneider, R. Kronland-Martinet and J. Morlet, Detection of abrupt changes in sound signals with the help of wavelet transforms, in:Inverse Problems (Academic Press, 1987).
S. Mallat, Zero-crossings of a wavelet transform, IEEE Trans. Inf. Theory IT-37 (1991).
S. Mallat and S. Zhong, Characterization of signals from multiscale edges, IEEE Trans. Pattern Anal. Machine Int. PAMI-14 (1992).
S. Mallat and W. Liang Hwang, Singularity detection and processing with wavelets, IEEE Trans. Inf. Theory IT-38 (1992).
Y. Meyer,Wavelets: Algorithms and Applications (SIAM, 1993).
P.J. Laurent, Inf.-convolution spline pour l'approximation de données discontinues, R.R. No.270, IMAG, Grenoble, France (1981).
P.J. Laurent, Inf-convolution splines, R.R. No. 749-M, IMAG, Grenoble, France (1988).
P.J. Laurent and F.I. Utreras, Optimal smoothing of noise broken data, Approx. Theory Appl. 2 (1986).
G. Wahba,Spline Models for Observational Data, CBMS-NSF, Regional Conference Series in Applied Mathematics (SIAM, 1990).
E. Quak and N. Weyrich, Decomposition and reconstruction algorithms for spline wavelets on a bounded interval, Appl. Comp. Harmonic Anal. 1 (1994) 217–231.
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Communicated by C.A. Micchelli
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Varas, M.L.S. Reconstruction of signals from multiscale edges. Adv Comput Math 5, 31–49 (1996). https://doi.org/10.1007/BF02124734
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DOI: https://doi.org/10.1007/BF02124734