Wavelet thresholding techniques for power spectrum estimation

Estimation of the power spectrum S( f ) of a stationary random process can be viewed as a nonparametric statistical estimation problem. We introduce a nonparametric approach based on a wavelet representation for the logarithm of the unknown S( f ). This approach offers the ability to capture statistically significant components of lnS( f ) at different resolution levels and guarantees nonnegativity of the spectrum estimator. The spectrum estimation problem is set up as a problem of inference on the wavelet coefficients of a signal corrupted by additive non-Gaussian noise. We propose a wavelet thresholding technique to solve this problem under specified noise/resolution tradeoffs and show that the wavelet coefficients of the additive noise may be treated as independent random variables. The thresholds are computed using a saddle-point approximation to the distribution of the noise coefficients. EDICS: 3.1.1, 2.2.1, 2.2.4 Index terms : wavelets, spectrum estimation, noise reduction, non-Gaussian signal processing.