Seismic data denoising through multiscale and sparsity-promoting dictionary learning

Seismic data comprise many traces that provide a spatiotemporal sampling of the reflected wavefield. However, such information maysuffer from ambient and random noise during acquisition, which could possibly limit the use of seismic data in reservoir locating. Traditionally, fixed transforms are used to separate the noise from the data by exploiting their different characteristics in a transform domain. However, their performance may not be satisfactory due to their lack of adaptability to changing data structures. We have developed a novel seismic data denoising method based on a parametric dictionary learning scheme. Unlike previous dictionary learning methods that had to learn unconstrained atoms, our method exploits the underlying sparse structure of the learned atoms over a base dictionary and significantly reduces the dictionary elements that need to be learned. By combining the advantages of multiscale representations with the power of dictionary learning, more degrees of freedom could be provided to the sparse representation, and therefore the characteristics of seismic data could be efficiently captured in sparse coefficients for denoising. The dictionary learning and denoising were processed from all overlapping patches of the given noisy seismic data, which maintained low complexity. Numerical experiments on synthetic seismic data indicated that our scheme achieved the best denoising performance in terms of peak signal-to-noise ratio and minimizes visual distortion.