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

This paper investigates 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 √(2 logN) σ, where σ is the noise standard deviation. The paper contains an original proof for this asymptotic behavior as well as an intuitive explanation. This behavior is necessary to prove the asymptotic optimality of a generalized cross validation procedure in estimating the minimum risk threshold.nrpages: 25status: publishe