Abstract
The aim of this paper is to present numerical results for noise reduction performed by modified wavelet reconstruction. The paper addresses the automatic choice of the related threshold/shrinkage parameter without any prior knowledge about the noise variance. We show that the cross validation method can be a helpful tool for making this choice. We give numerical examples using orthogonal and semi-orthogonal wavelets.
The authors were partially supported by fundings H98230-R5–92–9740 and H98230-R5–93–9187 from The U. S. Department of Defense, Ft. Meade, MD.
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References
Chui, C. K. (1992) An Introduction to Wavelets, Academic Press, Boston.
Chui, C. K. and Quak, E. (1992) Wavelets on a Bounded Interval, in Numerical Methods of Approximation Theory, Vol. 9, D. Braess and L. L. Schumaker (eds.), Birkhäuser, Basel.
Daubechies, I. (1992) Ten Lectures on Wavelets, CBMS-NSF Series in Appl. Math., SIAM Publications, Philadelphia.
Donoho, D. L. and Johnstone, I. M. (1992) Adapting to Unknown Smoothness via Wavelet Shrinkage, Technical Report, Department of Statistics, Stanford University.
Donoho, D. L. and Johnstone, I. M. (1992) Ideal Spatial Adaptation by Wavelet Shrinkage, Technical Report, Department of Statistics, Stanford University.
Hall, P. and Koch, I. (1992) On the Feasibility of Cross-Validation in Image Analysis, SIAM J. Appl. Math, 52 (1), 292–313.
Nason, G. P. (1994) Wavelet Regression by Cross-Validation, Technical Report, Department of Mathematics, University of Bristol, Bristol (UK).
Quak, E. and Weyrich, N. (1994) Decomposition and Reconstruction Algorithms for Spline Wavelets on a Bounded Interval, Appl. and Comp. Harmonic Analysis, 1, 217–231.
Stein, C. (1981) Estimation of the Mean of a Multivariate Normal Distribution, Annals of Statistics, 9 (6), 1135–1151.
Tasche, M. and Weyrich, N. (1993) Smoothing Inversion of Fourier Series Using Generalized Cross Validation, CAT Report #320, Department of Mathematics, Texas A&M University.
Wahba, G. (1990) Spline Models for Observational Data, SIAM, Philadelphia, Pennsylvania.
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© 1995 Springer Science+Business Media Dordrecht
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Weyrich, N., Warhola, G.T. (1995). De-Noising Using Wavelets and Cross Validation. In: Singh, S.P. (eds) Approximation Theory, Wavelets and Applications. NATO Science Series, vol 454. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8577-4_36
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DOI: https://doi.org/10.1007/978-94-015-8577-4_36
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4516-4
Online ISBN: 978-94-015-8577-4
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