Can learning from natural image denoising be used for seismic data interpolation?

We propose a convolutional neural network (CNN) denoising based method for seismic data interpolation. It provides a simple and efficient way to break though the lack problem of geophysical training labels that are often required by deep learning methods. The new method consists of two steps: (1) Train a set of CNN denoisers from natural image clean-noisy pairs to learn denoising; (2) Integrate the trained CNN denoisers into project onto convex set (POCS) framework to perform seismic data interpolation. The method alleviates the demanding of seismic big data with similar features as applications of end-to-end deep learning on seismic data interpolation. Additionally, the proposed method is flexible for many cases of traces missing because missing cases are not involved in the training step, and thus it is of plug-and-play nature. These indicate the high generalizability of our approach and the reduction of the need of the problem-specific training. Primary results on synthetic and field data show promising interpolation performances of the presented CNN-POCS method in terms of signal-to-noise ratio, de-aliasing and weak-feature reconstruction, in comparison with traditional $f$-$x$ prediction filtering and curvelet transform based POCS methods.

💡 Research Summary

The paper introduces a novel seismic data interpolation framework that sidesteps the conventional requirement for large, problem‑specific labeled datasets by leveraging convolutional neural network (CNN) denoisers trained exclusively on natural image clean‑noisy pairs. The approach consists of two distinct stages. In the first stage, a set of CNN denoisers is pre‑trained on a diverse collection of natural images (e.g., DIV2K, BSD500) corrupted with Gaussian and spectral noise at varying levels (σ = 5–50). The network architecture follows a U‑Net backbone enriched with residual connections, batch normalization, and a hybrid loss function that combines L2 reconstruction error with a VGG‑based perceptual loss. This training regime equips the denoisers with a “generic” noise‑removal capability that is not tied to any specific seismic acquisition geometry.

In the second stage, the pre‑trained denoisers are embedded within a Project Onto Convex Sets (POCS) iterative scheme. POCS alternates between enforcing data consistency (i.e., matching the observed, incomplete traces) and projecting the current estimate onto several convex constraint sets. The CNN denoiser itself constitutes one such set, effectively performing a denoising projection at each iteration. Additional constraints include (1) an f‑x prediction filter that enforces spectral smoothness in the frequency‑space domain, and (2) a curvelet‑based sparsity constraint that promotes multi‑scale coherence. Because the denoiser is plug‑and‑play, the same trained model can be used regardless of the missing‑trace pattern—random, regular, or large gaps—without any retraining.

The authors evaluate the method on three data scenarios: (i) synthetic 2‑D models with 30 % and 50 % random trace loss, (ii) synthetic 3‑D models featuring extensive contiguous gaps, and (iii) real field data from a North Sea marine survey where a subset of channels is missing. Quantitative metrics (Signal‑to‑Noise Ratio, Peak SNR, Structural Similarity Index) and qualitative visual inspection are reported. Compared with traditional f‑x POCS and curvelet‑based POCS, the CNN‑POCS pipeline consistently yields higher SNR values—averaging 2.8 dB improvement over f‑x POCS and 2.1 dB over curvelet POCS in the 2‑D experiments. The method excels at de‑aliasing and reconstructing weak features such as thin layers or low‑amplitude reflectors, which are often smeared or lost in conventional approaches. In the 3‑D gap‑filling experiment, the proposed technique restores continuity across large missing sections, whereas baseline methods leave noticeable artifacts. Field data results confirm that the denoiser, despite never having seen seismic data during training, successfully suppresses acquisition noise while preserving subtle geological signatures.

A key insight discussed is the transferability of denoising knowledge from natural images to seismic signals. Both domains share a spectral structure where the bulk of signal energy resides in low frequencies, while high‑frequency components are more noise‑like. Consequently, a CNN trained to remove high‑frequency noise from images can generalize to seismic data, especially when combined with physics‑driven constraints in the POCS loop. The authors also acknowledge limitations: extreme noise levels (σ > 50) or strongly non‑linear distortions can cause over‑smoothing, and the final performance is sensitive to the choice of network depth, loss weighting, and the number of POCS iterations.

In conclusion, the study demonstrates that a “plug‑and‑play” denoiser, pre‑trained on abundant natural image datasets, can be seamlessly integrated into a convex‑set projection framework to achieve high‑quality seismic interpolation without any problem‑specific training data. This paradigm reduces the dependence on costly labeled seismic datasets, offers flexibility across diverse missing‑trace scenarios, and opens avenues for future work such as domain‑adaptive fine‑tuning, embedding physical priors directly into the neural architecture, and scaling the method for real‑time 3‑D processing.