Denoising of Seismic Signals via Bayes Theorem with Wavelet Packet Bases

An application of Bayes theorem to seismic signal ltering is implemented. A best basis strategy is derived as an hypothesis test with maximum entropy priors. Cost functionals are derived. In this approach the best basis is determined as the basis least likely to t the prior noise model. Sub-band varianace estimates contain all of the information regarding the background noise. A Bayes estimator is derived based on this notion of best basis and it is shown to be an adaptive shrinkage operator of wavelet coeecients. Adaptation results from the recursive estimation of sub-band noise variances. Estimation of these subband variances must be extremely robust and therefore event hypothesis tests must be used to choose between estimator types. The algorithm is tested on synthetic seismic events and on real seismic data for its capacity for noise rejection and signal delity.