Comparisons of wavelets, contourlets and curvelets in seismic denoising

Seismic synthetic records represent wave-front components which contain abundant damageable directional information about important geologic substances. However, the information is often polluted by random noises. Unlike coherent noise, random noise may be incoherent in space and time, and sometimes unpredictable. One of the main tasks in seismic denoising is to eliminate the random noise and useless interferential wave components while preserving or recovering the important seismic features. In this paper, we investigate multi-resolution (MR) methods including wavelets, contourlets and curvelets for seismic denoising of random noise. Discussions and interpretations for these methods are presented in detail to evaluate their performances. Furthermore, a combination scheme of wavelets and curvelets is applied to seismic random denoising by solving an l₁ norm optimization problem. The combined scheme aims at taking advantage of the respective merits of wavelets and curvelets in order to obtain better effects. Experimental results indicate that the directional wavelets such as contourlets and curvelets are prominent for seismic profiles containing textural features and the combination method shows promising performances than individual transforms.