Fast and accurate dictionary learning for seismic data denoising using convolutional sparse coding

Seismic data inevitably suffers from random noise sources in field acquisition. This could potentially limit its utilization for subsequent imaging or inversion applications. Recently, dictionary learning has gained remarkable success in seismic data denoising. Variants of the patch-based learning technique, such as the K-SVD algorithm, have been shown to improve denoising performance compared to 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. By contrast, the Convolutional Sparse Coding (CSC) model treats the signals globally and, therefore, has shown superior performance over patch-based methods in several image processing applications. Here, we propose the use of CSC model for seismic data denoising. In particular, we use the Local Block Coordinate Descent (LoBCoD) algorithm to reconstruct clean seismic data from noisy input data. We compare denoising performance of the LoBCoD algorithm with that of K-SVD. We use two quality measures to test the denoising accuracy: the peak signal-to-noise ratio (PSNR) and the relative L₂-norm of the error (RLNE). We find that LoBCoD performs better than K-SVD for all test cases in improving PSNR and reducing RLNE. Moreover, we find the LoBCoD algorithm to be computationally cheaper than the K-SVD algorithm for our test cases. These observations suggest the enormous potential of the CSC model in seismic data denoising applications.