Title :
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
fDate :
6/1/2001 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
