xxx SEISMIC DATA FILTERING WITH HIERARCHICAL LAPPED TRANSFORMS AND HIDDEN MARKOV MODELS
Laurent C. Duval · 2003
We propose a method for uncoherent noise removal in geophysical data. The Multiple Wavelet Stacking is based on a concurrent use of wavelet-based shrinkage and data and time-scale depen-dent threshold choice. Since one singular wavelet does not match all the time-varying properties of a signal, the simultaneous use of several wavelets is able to lower some shrinkage shortcomings, such as wavelet dependency, and to further reduce the residual noises. Motivation and related works Wavelet transforms have emerged as efficient tools for signal separation and noise filtering in several geophysical applications. In heavy noise conditions, wavelet-based techniques generally owe their robustness to their attractive time-scale properties. Wavelet based denoising, or wavelet shrinkage [Miao and Cheadle, 1998], arises from the work of D. Donoho, based on the energy compaction properties of these time-scale operators [Donoho, 1995]. With the most widely used signal model [Ulrych et al., 1999], let R represent an actual geophysical record. It can be decom-posed in an underlying signal S, and two noise components N