In this section, several synthetic and field data examples will be used to test the validity of the proposed method. We will use examples containing both crossing linear events and hyperbolic events to test the sensitivity of methods to different data structures. For synthetic examples, we use the signal-to-noise ratio (SNR) metric for quantitative evaluation, which is defined as follows:

SNR(dB)$\displaystyle =10\log_{10}\frac{\Arrowvert \mathbf{S} \Arrowvert_F^2}{\Arrowvert \mathbf{S} -\hat{\mathbf{S}}\Arrowvert_F^2}.$ (23)

where $\hat{\mathbf{S}}$ and $\mathbf{S}$ denote the estimated signal and exact solution, respectively. In addition, we use the local similarity attribute (Chen and Fomel, 2015) to measure the damage that a denoising method can cause to seismic data. In general, higher local similarity between the denoised data and removed noise indicates greater damages. The local similarity attribute allows to quantify the effectiveness of a denoising algorithm on datasets when the exact solution is unknown. The local similarity can also measure the local orthogonality between the separated signal and noise components (Chen and Fomel, 2015). Here, we assume that the signal and noise components should be locally orthogonal, which is indicated by low anomalies in the local similarity maps. Processing pre-stack seismic data is much more challenging than that for post-stack seismic data. Subtle diffraction signals could be treated as noise by the algorithm and be attenuated, potentially damaging images along faults. In this paper, we only focus on the denoising of post-stack seismic data, but further work could focus on noise attenuation of pre-stack data.