Unsupervised Erratic Seismic Noise Attenuation With Robust Deep Convolutional Autoencoders

Erratic seismic noise, following a (known or unknown) non-Gaussian distribution, poses a formidable challenge to conventional methods of random noise attenuation. Many erratic noise cancellation methods, for instance, robust reduced-rank and sparsity-promoting filtering, have been proven to achieve promising results in overcoming this challenge. Among them, deep learning (DL) methods require no assumptions about the underlying clear seismic image and are also more robust against erratic and random noise. However, the success of existing DL-based denoising methods strongly depends on supervised learning from a large number of ground-truth seismic images affected by erratic noise and their clean counterparts, which are typically unavailable in a real-world setting. As an alternative, this article presents an unsupervised DL method for erratic-plus-Gaussian noise removal based on a robust deep convolutional autoencoder (RDCAE). In the RDCAE, the mean squared error (mse) loss in a classic DCAE is replaced by the smooth Welsch function to exploit the concept of robust image denoising. In this way, the erratic noise is downweighted by means of a curbed weight defined in terms of the Welsch function. In contrast, the random noise is diluted by combining the mean square in the Welsch function and the total variation (TV). Subsequently, the training procedures required for solving the RDCAE are derived on the basis of the backpropagation (BP) algorithm for a neural network. Experiments conducted on both synthetic and real field datasets are reported to illustrate the efficacy of the proposed method.