Seismic Inpainting with Deep Priors

Problem

Seismic acquisition surveys routinely produce data with missing or corrupted traces due to hardware failures, terrain constraints, and acquisition cost trade-offs. Conventional interpolation (linear, spline, Fourier-based) fails when the missing fraction exceeds ~30% or when the spatial aliasing is severe.

Approach

We frame trace reconstruction as a regularised inverse problem. Rather than training a supervised model on labelled pairs, we exploit a deep generative prior: a U-Net initialised with random weights acts as a structural prior over the signal manifold. The network is optimised at test time to fit only the observed traces while its architecture implicitly regularises the solution.

The reconstruction loss is:

$\mathcal{L} = \|\mathbf{M} \odot (f_\theta(\mathbf{z}) - \mathbf{y})\|_2^2 + \lambda \|\nabla f_\theta(\mathbf{z})\|_1$

where $\mathbf{M}$ is the binary observation mask, $f_\theta$ is the U-Net, $\mathbf{z}$ is a fixed noise seed, and $\lambda$ controls total-variation regularisation.

Results

Evaluated on the SEAM Phase I synthetic dataset with 40% random trace removal:

• PSNR: 28.4 dB (ours) vs 25.2 dB (conventional POCS interpolation) — +3.2 dB
• SSIM: 0.91 vs 0.83
• Convergence: ~800 gradient steps per patch on a single A100

Tech stack

PyTorch, NumPy, SciPy, Matplotlib, custom CUDA kernels for the observation mask operator.

Status

Paper accepted at IEEE Transactions on Geoscience and Remote Sensing (2024, pending publication).