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

This paper investigates the asymptotic behavior of the minimum-risk thresho ld for wavelet coefficients with additive, homoscedastic, Gaussian noise an d 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 s tandard 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 estimat e the minimum risk threshold.