3-D Seismic Noise Attenuation via Tensor Sparse Coding With Spatially Adaptive Coherence Constraint

Tensor sparse coding (TSC) is a method used to excavate 3D volume structures extended by sparse coding (SC), which is increasingly applied in data noise attenuation. Existing TSC approaches control the intensity of noise attenuation by using a predetermined soft or hard threshold that relies on the noise variance. However, the noise variance in seismic data is unknown and varies with time and space, leading to the conventional TSC method not being able to track this change. To address this issue, we proposed a tensor sparse coding model with spatially adaptive coherent constraint (TSC-SAC) to find an optimal adjustable threshold without the demand for prior knowledge of the noise variance. The threshold is determined by the coherence of the residual with respect to the dictionary. Moreover, a tensor spatial coherence orthogonal matching pursuit algorithm (TSC-OMP) is developed for solving sparse representation. Unlike the existing threshold strategy in traditional TSC methods, TSC-OMP utilizes an ideal spatially adaptive coherence threshold to regulate the sparsity, which can effectively preserve the valuable information in processing for noise suppression. By comparing with four state-of-the-art denoising algorithms, we then demonstrated the superior performance of TSC-SAC on both a synthetic and two field data sets.