Seismic signal denoising using model selection

We consider the determination of a soft wavelet threshold for the recovery of a signal embedded in additive Gaussian noise. This is closely related to the problem of variable selection in an orthogonal normal linear regression. Viewing the denoising problem as a model selection one, we first construct a statistical model for the unknown signal and then try to find the best approximating model (corresponding to the denoised signal) from a class of candidates. We adopt the Kullback symmetric divergence as a measure of similarity between the unknown model and the candidate model. The best approximating model is the one that minimizes an unbiased estimator of this divergence. The advantage of denoising methods based on model selection over classical approaches, resides in the fact that the threshold is determined automatically without the need to estimate the noise variance. The proposed denoising methods, called KICc-denoising is compared with Cross Validation (CV), Minimum Description Length (MDL) and the classical methods SureShrink and VisuShrink in a simulation study to treat the problem of seismic signal denoising.