Asymptotic behavior of the minimum mean squared error threshold for noisy wavelet coefficients of piecewise smooth signals

Author

Jansen, Maarten ; Bultheel, Adhemar

Author_Institution

Dept. of Comput. Sci., Belgian Found. for Sci. Res., Heverlee, Belgium

Volume

49

Issue

6

fYear

2001

fDate

6/1/2001 12:00:00 AM

Firstpage

1113

Lastpage

1118

Abstract

This paper investigates the asymptotic behavior of the minimum risk threshold for wavelet coefficients with additive, homoscedastic, Gaussian noise and for a soft-thresholding scheme. We start from N samples from a signal on a continuous time axis. For piecewise smooth signals and for N→∞, this threshold behaves as C√(2logN)σ, where σ is the noise standard-deviation. The paper contains an original proof for this asymptotic behavior as well as an intuitive explanation. The paper also discusses the importance of this asymptotic behavior for practical cases when we estimate the minimum risk threshold

Keywords

Gaussian noise; least mean squares methods; parameter estimation; polynomials; signal sampling; smoothing methods; wavelet transforms; MMSE threshold; additive homoscedastic Gaussian noise; asymptotic behavior; continuous time axis; digital signals; minimum mean squared error threshold; minimum risk threshold estimation; noise standard-deviation; noisy wavelet coefficients; piecewise polynomials; piecewise smooth signals; signal samples; soft-thresholding; universal threshold; wavelet coefficients; Additive noise; Computer science; Gaussian noise; Mean square error methods; Noise reduction; Random variables; Statistics; Vectors; Wavelet coefficients; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.923292

Filename

923292