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 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/spl rarr//spl infin/, this threshold behaves as C/spl radic/(2logN)/spl sigma/, where /spl 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.