Random noise attenuation in 3D seismic data by iterative block tensor singular value thresholding

The principal component analysis (PCA) is one of the most widely used technique in two-dimensional data analysis which uses singular value decomposition of matrix data and extracts its low-rank components. Using the PCA, seismic signals are represented in a sparse way which is a useful and popular methodology in signal-processing applications. Tensor principal component analysis (TPCA) as a multi-linear extension of principal component analysis, converts a set of correlated measurements into several principal components. In this paper, based on the singular value decomposition and extracting low-rank component as the denoised data, we used a new version of TPCA for denoising 3D seismic data in which, tensor data split into a number of blocks of the same size. The low-rank component of each block tensor is extracted using iterative tensor singular value thresholding method. The principal components of the multi-way data are the concatenation of all the low-rank components of all the block tensors. To demonstrate the performance of the proposed method for denoising 3D seismic data, we apply it to a 3D synthetic seismic data and a 3D real seismic data.