Title: Asymptotic behavior of the minimum mean squared error treshold for noisy wavelet coefficients of piecewise smooth signals
Authors: Jansen, Maarten ×
Bultheel, Adhemar
Issue Date: Oct-1999
Publisher: Department of Computer Science, K.U.Leuven
Series Title: TW Reports vol:TW294
Abstract: 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.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author

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