Deep learning for denoising

Abstract: Compared with traditional seismic noise attenuation algorithms that depend on signal models and their corresponding prior assumptions, removing noise with a deep neural network is trained based on a large training set, where the inputs are the raw datasets and the corresponding outputs are the desired clean data. After the completion of training, the deep learning method achieves adaptive denoising with no requirements of (i) accurate modelings of the signal and noise, or (ii) optimal parameters tuning. We call this intelligent denoising. We use a convolutional neural network as the basic tool for deep learning. In random and linear noise attenuation, the training set is generated with artificially added noise. In the multiple attenuation step, the training set is generated with acoustic wave equation. Stochastic gradient descent is used to solve the optimal parameters for the convolutional neural network. The runtime of deep learning on a graphics processing unit for denoising has the same order as the $f-x$ deconvolution method. Synthetic and field results show the potential applications of deep learning in automatic attenuation of random noise (with unknown variance), linear noise, and multiples.