# Total-variation regularization strategies in full-waveform inversion

arXiv: https://arxiv.org/abs/1608.06159 · HTML: https://mlsanity.com/paper/1608.06159/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2016.

## Built on by (most cited first, 18 of 18)

- [Implicit Full Waveform Inversion with Deep Neural Representation](https://mlsanity.com/paper/2209.03525/) (2022)
- [ASPIRE: Iterative Amortized Posterior Inference for Bayesian Inverse Problems](https://mlsanity.com/paper/2405.05398/) (2024)
- [Solving multiphysics-based inverse problems with learned surrogates and constraints](https://mlsanity.com/paper/2307.11099/) (2023)
- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion](https://mlsanity.com/paper/2509.21659/) (2025)
- [Real-Time Model-Based Quantitative Ultrasound and Radar](https://mlsanity.com/paper/2402.10520/) (2024)
- [Diffusion prior as a direct regularization term for FWI](https://mlsanity.com/paper/2506.10141/) (2025)
- [Dual-space posterior sampling for Bayesian inference in constrained inverse problems](https://mlsanity.com/paper/2603.00393/) (2026)
- [Decoupled Latent Optimization of Diffusion Models for Full Waveform Inversion](https://mlsanity.com/paper/2606.14139/) (2026)
- [GPR Full-Waveform Inversion through Adaptive Filtering of Model Parameters and Gradients Using CNN](https://mlsanity.com/paper/2410.08568/) (2024)
- [Unveiling the Mechanism of Continuous Representation Full-Waveform Inversion: A Wave Based Neural Tangent Kernel Framework](https://mlsanity.com/paper/2603.22362/) (2026)
- [Object based Bayesian full-waveform inversion for shear elastography](https://mlsanity.com/paper/2305.06646/) (2023)
- [Simultaneous Automatic Picking and Manual Picking Refinement for First-Break](https://mlsanity.com/paper/2502.01474/) (2025)
- [Total Generalized Variation regularization closes the gap between neural-eld and classical methods in seismic travel-time tomography](https://mlsanity.com/paper/2605.09960/) (2026)
- [Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel](https://mlsanity.com/paper/2605.14370/) (2026)
- [Extending Occam's inversion with lasso fusion, overcomplete dictionaries, and isotropic total variation regularisation](https://mlsanity.com/paper/2608.14225/) (2026)
- [Physical-State-Guided Diffusion Sampling for Full-Waveform Inversion](https://mlsanity.com/paper/2609.12899/) (2026)
- [Full Waveform Inversion with a Learned Preconditioner](https://mlsanity.com/paper/2610.15331/) (2026)

## Abstract (arXiv)

We propose an extended full-waveform inversion formulation that includes general convex constraints on the model. Though the full problem is highly nonconvex, the overarching optimization scheme arrives at geologically plausible results by solving a sequence of relaxed and warm-started constrained convex subproblems. The combination of box, total-variation, and successively relaxed asymmetric total-variation constraints allows us to steer free from parasitic local minima while keeping the estimated physical parameters laterally continuous and in a physically realistic range. For accurate starting models, numerical experiments carried out on the challenging 2004 BP velocity benchmark demonstrate that bound and total-variation constraints improve the inversion result significantly by removing inversion artifacts, related to source encoding, and by clearly improved delineation of top, bottom, and flanks of a high-velocity high-contrast salt inclusion. The experiments also show that for poor starting models these two constraints by themselves are insufficient to detect the bottom of high-velocity inclusions such as salt. Inclusion of the one-sided asymmetric total-variation constraint overcomes this issue by discouraging velocity lows to buildup during the early stages of the inversion. To the author's knowledge the presented algorithm is the first to successfully remove the imprint of local minima caused by poor starting models and band-width limited finite aperture data.