A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

TL;DR

This paper introduces a primal-dual proximal algorithm for adaptive seismic filtering that effectively separates signals from complex noise using sparse representations and inaccurate templates, improving performance in low SNR conditions.

Contribution

It presents a novel convex variational framework and primal-dual algorithm for joint estimation of adaptive filters and signals using sparse wavelet frames, handling inaccurate templates.

Findings

Effective in low SNR seismic data

Performs well on simulated and real data

Addresses hyperparameter regularization issues

Abstract

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data.