IEEE transactions on signal processing vol:49 issue:6 pages:1113-1118
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 --> infinity, this threshold behaves as C root 2log N sigma, where sigma 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.