Seismic Denoising Based on Dictionary Learning With Double Regularization for Random and Erratic Noise Attenuation

In seismic data processing, denoising is one of the essential steps to identifying the earth’s subsurface layer information. The noise present in the seismic data is categorized into two types: random and erratic noise. The random noise is distributed uniformly over the seismic data. The erratic noise attenuation is always challenging due to the unknown distribution of high-amplitude peaks over seismic data. The existing double sparsity dictionary learning (DSDL) method performs with analytical and adaptive transforms; both the transforms include iterative algorithms with K-singular-value decomposition (SVD); it is computationally costly, and the dictionary is initialized with trained data. To address these limitations, we propose a novel method of dictionary learning with double regularization (DLDR) to denoise both random and erratic noise from seismic data. In double regularization, we used with $\ell _{1}$ -norm and nuclear norm. The denoised data is applied to the alternating direction method of multipliers (ADMMs) to improve denoising while preserving the signal features from seismic data while reducing the computational cost. We evaluated the performance of the proposed method using signal-to-noise ratio (SNR), mean squared error (MSE), and local similarity map. The numerical results demonstrated that the proposed method resulted in higher SNR, lower MSE, and less signal leakage from seismic data. The method gives precise interpretation from the denoised seismic data.