Dictionary learning with convolutional structure for seismic data denoising and interpolation

Seismic data inevitably suffer from random noise and missing traces in field acquisition. This limits the use of seismic data for subsequent imaging or inversion applications. Recently, dictionary learning has gained remarkable success in seismic data denoising and interpolation. Variants of the patch-based learning technique, such as the K-singular value decomposition (K-SVD) algorithm, have been shown to improve denoising and interpolation performance compared with the analytic transform-based methods. However, patch-based learning algorithms work on overlapping patches of data and do not take the full data into account during reconstruction. In contrast, the data patches (convolutional sparse coding [CSC]) model treats signals globally and, therefore, has shown superior performance over patch-based methods in several image processing applications. As a consequence, we test use of the CSC model for seismic data denoising and interpolation. In particular, we use the local block coordinate descent (LoBCoD) algorithm to reconstruct missing traces and clean seismic data from noisy input. The denoising and interpolation performance of the LoBCoD algorithm has been compared with that of K-SVD and orthogonal matching pursuit (OMP) algorithms using synthetic and field data examples. We have used three quality measures to test the denoising accuracy: the peak signal-to-noise ratio (PS/N), the relative L2-norm of the error (RLNE), and the structural similarity index (SSIM). We find that LoBCoD performs better than K-SVD and OMP for all test cases in improving PS/N and SSIM and in reducing RLNE. These observations suggest a huge potential of the CSC model in seismic data denoising and interpolation applications.