Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Models

2024-08-05

arXiv.org

AI Summary

This work addresses the broadband inverse scattering problem by proposing the first probabilistic framework that jointly incorporates physical symmetry constraints and conditional diffusion modeling to efficiently approximate the refractive index posterior distribution from wideband scattering data. The method adopts a two-stage architecture: (i) a physics-informed, low-rank latent representation is generated via filtered backprojection; (ii) a conditional diffusion score function is learned over this representation. Key innovations include symmetry-aware embedding and a compressible-rank latent space, enabling sublinear parameter growth with resolution, enhanced training stability, and sub-Nyquist feature recovery. Experiments demonstrate high accuracy, high spatial resolution, and sharp reconstructions—even under strong multiple-scattering regimes—while significantly reducing sample complexity, computational cost, and eliminating the need for post-processing.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution of the refractive index using the wideband scattering data through the inverse scattering map. 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, with the first, inspired by the filtered back-propagation formula, transforms data into a physics-based latent representation, while the second 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.

Problem

• Wideband inverse scattering problem
• Refractive index posterior distribution
• Sub-Nyquist feature recovery

Innovation

• Uses conditional diffusion models
• Incorporates filtered back-projection formula
• Learns conditional score function