Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Models
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913843101302784 |
|---|---|
| author | Zhang, Borong Guerra, Martín Li, Qin Zepeda-Núñez, Leonardo |
| author_facet | Zhang, Borong Guerra, Martín Li, Qin Zepeda-Núñez, Leonardo |
| contents | We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate reconstructions, leveraging conditional diffusion models to draw samples, and also honors the symmetries of the underlying physics of wave-propagation. The procedure is factored into two steps: the first step, inspired by the filtered back-propagation formula, transforms data into a physics-based latent representation, while the second step learns a conditional score function conditioned on this latent representation. These two steps individually obey their associated symmetries and are amenable to compression by imposing the rank structure found in the filtered back-projection formula. Empirically, our framework has both low sample and computational complexity, with its number of parameters scaling only sub-linearly with the target resolution, and has stable training dynamics. It provides sharp reconstructions effortlessly and is capable of recovering even sub-Nyquist features in the multiple-scattering regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Models Zhang, Borong Guerra, Martín Li, Qin Zepeda-Núñez, Leonardo Machine Learning Numerical Analysis We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate reconstructions, leveraging conditional diffusion models to draw samples, and also honors the symmetries of the underlying physics of wave-propagation. The procedure is factored into two steps: the first step, inspired by the filtered back-propagation formula, transforms data into a physics-based latent representation, while the second step learns a conditional score function conditioned on this latent representation. These two steps individually obey their associated symmetries and are amenable to compression by imposing the rank structure found in the filtered back-projection formula. Empirically, our framework has both low sample and computational complexity, with its number of parameters scaling only sub-linearly with the target resolution, and has stable training dynamics. It provides sharp reconstructions effortlessly and is capable of recovering even sub-Nyquist features in the multiple-scattering regime. |
| title | Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Models |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2408.02866 |