Subspace Diffusion Posterior Sampling for Travel-Time Tomography
<|reference_start|>Subspace Diffusion Posterior Sampling for Travel-Time Tomography: Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical solvers for gradient updates. Although diffusion-based sampling methods can produce high-quality reconstructions, challenges persist in nonlinear PDE-based inverse problems and sampling speed. In this work, we explore solving PDE-based travel-time tomography based on subspace diffusion generative models. Our main contributions are twofold: First, we propose a posterior sampling process for PDE-based inverse problems by solving the associated adjoint-state equation. Second, we resorted to the subspace-based dimension reduction technique for conditional sampling acceleration, enabling solving the PDE-based inverse problems from coarse to refined grids. Our numerical experiments showed satisfactory advancements in improving the travel-time imaging quality and reducing the sampling time for reconstruction.<|reference_end|>
@article{cao2024subspace,
    title={Subspace Diffusion Posterior Sampling for Travel-Time Tomography},
    author={Xiang Cao, Xiaoqun Zhang},
    journal={arXiv preprint arXiv:2408.17333},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.17333},
    primaryClass={math.NA cs.NA math.AP}
}