Learned Proximal Operator for Solving Seismic Deconvolution Problem

TL;DR

This paper introduces LP4SD, a neural network-based learned proximal operator for seismic deconvolution, improving reconstruction quality over traditional methods by learning complex regularizers from synthetic data.

Contribution

The paper presents a novel learned proximal operator approach for seismic deconvolution that learns complex regularizers directly from data, outperforming traditional regularization techniques.

Findings

LP4SD achieves better reconstruction metrics than direct inverse methods.

The method generalizes well to both synthetic and real seismic data.

Training on synthetic data effectively captures complex structures for deconvolution.

Abstract

Seismic deconvolution is an essential step in seismic data processing that aims to extract layer information from noisy observed traces. In general, this is an ill-posed problem with non-unique solutions. Due to the sparse nature of the reflectivity sequence, spike-promoting regularizers such as the $\ell_1$-norm are frequently used. They either require rigorous coefficient tuning or strong assumptions about reflectivity, such as assuming reflectivity as sparse signals with known sparsity levels and zero-mean Gaussian noise with known noise levels. To overcome the limitations of traditional regularizers, learning-based regularizers are proposed in the recent past. This paper proposes a Learned Proximal operator for Seismic Deconvolution (LP4SD), which leverages a neural network to learn the proximal operator of a regularizer. LP4SD is trained in a loop unrolled manner and is capable of learning complicated structures from the training data. It is worth mentioning that the network is trained with synthetic data and evaluated on both synthetic and real data. LP4SD is shown to generate better reconstruction results in terms of three different metrics as compared to learning a direct inverse.