Simultaneous Sparse and Low-Rank Regularization for Seismic Data Denoising

The denoising problem of multidimensional seismic data can be regarded as a low-rank tensor decomposition problem. However, seismic data only has many ranks close to zero, which does not meet the definition of low-rank data. Adding low-rank constraints to the data will result in the loss of some features of the data. To overcome this problem, this letter proposes a nearly low-rank tensor decomposition method (NLRTD) for seismic data denoising. First, differing from existing low-rank-based methods, we consider a nearly low-rank approximation, which is closer to the latent low-rank structure of the clean data. Then, we exploit a simultaneously sparse and low-rank tensor representation model to enhance the capability of dictionary learning and use the alternating direction method of multipliers (ADMMs) algorithm to obtain denoising results. In the experimental part, we test the 3-D seismic data. Compared with the higher-order singular value decomposition (HOSVD) and low-rank tensor dictionary learning (LTDL) methods, the method in this letter achieves better denoising results.