Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel

TL;DR

This paper introduces a theoretical framework using neural sensitivity and wave tangent kernels to analyze and improve neural reparameterized full-waveform inversion, enhancing convergence and efficiency in seismic and medical imaging.

Contribution

It establishes the neural sensitivity kernel and wave tangent kernel to explain the convergence behavior of NeurFWI and proposes methods to optimize their eigen-structures for better performance.

Findings

Neural tangent kernel modulates sensitivity and wave tangent kernels.

Spectral filtering and frequency bias affect convergence.

Proposed methods improve inversion efficiency and accuracy.

Abstract

Full-waveform inversion (FWI) estimates unknown parameters in the wave equation from limited boundary measurements. Recent advances in neural reparameterized FWI (NeurFWI) demonstrate that representing the parameters using a neural network can reduce the reliance on the high-quality initial model and wavefield data, at the cost of slow high-resolution convergence. However, its underlying theoretical mechanism remains unclear. In this study, we establish the neural sensitivity kernel (NSK) and the wave tangent kernel (WTK) to analyze their convergence behavior from both model and data domains. These theoretical frameworks show that the neural tangent kernel (NTK) induced by neural representation adaptively modulates the original sensitivity and wave tangent kernels. This modulation leads to several key outcomes, i.e., the spectral filtering effect, the gradient wavenumber modulation, and the wave frequency bias, connecting the convergence behavior of NeurFWI with the eigen-structures of NSK and WTK. Building on these insights, we propose several enhanced NeurFWI methods with tailored eigen-structures in NSK and WTK to improve inversion performances and efficiency. We numerically validate these theoretical claims and the proposed methods in seismic exploration, and firstly extend their application to medical imaging.