DIP-MoG: Non-i.i.d. Seismic Noise Attenuation Using Mixture of Gaussians Noise Model and Deep Image Prior

Seismic data denoising is essential for subsequent inversion and interpretation tasks. However, most existing methods rely on loss functions that assume seismic noise follows an independent and identically distributed (i.i.d.) Gaussian distribution, which does not align with the characteristics of actual seismic noise. In this paper, we first analyze the principle of the L<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm loss function in suppressing i.i.d. Gaussian noise from the maximum a posteriori (MAP) perspective, and then introduce the Mixture of Gaussians (MoG) model to handle non-i.i.d. noise suppression. Additionally, we optimize the MoG model using the Expectation-Maximization (EM) algorithm for improved performance. We propose a novel approach, DIP-MoG, which integrates the Deep Image Prior (DIP) with the MoG model for enhanced denoising. To validate the performance of DIP-MoG, we conduct experiments on two synthetic datasets contaminated with a mixture of Gaussian noise and field noise, as well as a field seismic dataset. The results from both synthetic and field data demonstrate the superior denoising performance of DIP-MoG.