Joint Tensor Ring Decomposition and Unidirectional Total Variation for Seismic Data Denoising

Low-rank tensor approximation (LRTA) techniques have demonstrated great promise for seismic data denoising due to their ability to capture multi-dimensional dependencies. However, most existing methods fail to make full use of the correlations across different modes of tensors, leading to suboptimal denoising performance. In this paper, we propose a novel method, termed TR-UTV, which integrates tensor ring (TR) decomposition with unidirectional total variation (UTV) for highly effective seismic data denoising. The proposed TR-UTV approach exploits TR decomposition to capture the underlying low-rank (LR) structures of seismic data and integrates UTV to suppress footprint noise. Considering that real seismic data are typically non-stationary and contain complex noise patterns, a Laplacian scale mixture prior is employed to model sparse tensor coefficients, enabling joint estimation of both their values and variances. Additionally, an alternating direction method of multipliers (ADMM) algorithm is developed to effectively solve the proposed TR-UTV-based seismic data denoising problem. Extensive experiments on synthetic and field seismic data demonstrate that the proposed TR-UTV algorithm outperforms many state-of-the-art seismic data denoising methods in terms of both quantitative metrics and visual quality.