Seismic data denoising based on learning-type overcomplete dictionaries*
Tang Gang1,2, Ma Jian-Wei3, and Yang Hui-Zhu1
1. Institute of Seismic Exploration, School of Aerospace, Tsinghua University, Beijing 100084, China.
2. Geophysical Department, RIPED, PetroChina, Beijing 100083, China.
3. Institute of Applied Mathematics, Harbin Institute of Technology, Harbin 150001, China.
Abstract：
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 fi xed 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.
2012, Vol. 9 
