Seismic data denoising based on learning-type overcomplete dictionaries

The transform base function method is one of the most commonly used techniques for seismic denoising, which achieves the purpose of removing noise by utilizing the sparseness and separateness of seismic data in the transform base function domain. However, the effect is not satisfactory because it needs to pre-select a set of fixed transform-base functions and process the corresponding transform. In order to find a new approach, we introduce learning-type overcomplete dictionaries, i.e., optimally sparse data representation is achieved through learning and training driven by seismic modeling data, instead of using a single set of fixed transform bases. In this paper, we combine dictionary learning with total variation （TV） minimization to suppress pseudo-Gibbs artifacts and describe the effects of non-uniform dictionary sub-block scale on removing noises. Taking the discrete cosine transform and random noise as an example, we made comparisons between a single transform base, non-learning-type, overcomplete dictionary and a learning-type overcomplete dictionary and also compare the results with uniform and nonuniform size dictionary atoms. The results show that, when seismic data is represented sparsely using the learning-type overcomplete dictionary, noise is also removed and visibility and signal to noise ratio is markedly increased. We also compare the results with uniform and nonuniform size dictionary atoms, which demonstrate that a nonuniform dictionary atom is more suitable for seismic denoising.

Random seismic noise attenuation by learning-type overcomplete dictionary based on K-singular value decomposition algorithm

The transformation of basic functions is one of the most commonly used techniques for seismic denoising,which employs sparse representation of seismic data in the transform domain. The choice of transform base functions has an influence on denoising results. We propose a learning-type overcomplete dictionary based on the K-singular value decomposition( K-SVD) algorithm. To construct the dictionary and use it for random seismic noise attenuation,we replace fixed transform base functions with an overcomplete redundancy function library. Owing to the adaptability to data characteristics,the learning-type dictionary describes essential data characteristics much better than conventional denoising methods. The sparsest representation of signals is obtained by the learning and training of seismic data. By comparing the same seismic data obtained using the learning-type overcomplete dictionary based on K-SVD and the data obtained using other denoising methods,we find that the learning-type overcomplete dictionary based on the K-SVD algorithm represents the seismic data more sparsely,effectively suppressing the random noise and improving the signal-to-noise ratio.