Unsupervised erratic noise suppression in prestack seismic gathers via PnP-ADMM with implicit neural representation

Abstract Erratic noise in seismic data is characterized by high amplitude, non-Gaussian behavior and spatial incoherence, making it difficult to suppress using conventional filtering or supervised learning methods, which rely on statistical assumptions or access to clean ground truth. This paper introduces a novel unsupervised denoising framework based on the Plug-and-Play Alternating Direction Method of Multipliers (PnP-ADMM), incorporating an implicit neural representation (INR) as a trainable denoiser. The INR is implemented using the Sinusoidal Representation Network (SIREN) architecture: a coordinate-based multilayer perceptron with sinusoidal activation functions, which is trained for a fixed number of epochs and reused across ADMM iterations. ADMM is employed for its ability to decompose complex optimization problems into simpler subproblems, offering improved convergence control and flexibility in integrating nonconvex denoisers such as neural networks. The PnP formulation allows seamless incorporation of the SIREN denoiser into the iterative optimization loop without requiring an explicit prior model. By fitting the current signal estimate to spatiotemporal coordinates, SIREN leverages its spectral bias toward learning smooth, continuous structures, thereby avoiding the fitting of incoherent, high-frequency interference. This property is well-suited for seismic data, where useful signals are typically structured and erratic noise tends to be spatially irregular or unstructured. We evaluate the proposed method on two challenging types of erratic noise: swell noise and blended noise. The denoising problem is formulated as an unsupervised signal separation task, solved without requiring clean labels or pretrained models. Experimental results demonstrate that the PnP-ADMM framework with SIREN effectively suppresses erratic noise and preserves coherent seismic reflections, outperforming conventional denoising methods under challenging acquisition conditions.