We present \textit{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 leverages conditional diffusion models coupled with the underlying physics of wave-propagation and symmetries in the problem, to produce highly accurate reconstructions. The framework introduces a factorization of the score function into a physics-based latent representation inspired by the filtered back-propagation formula and a conditional score function conditioned on this latent representation. These two steps are also constrained to obey symmetries in the formulation while being amenable to compression by imposing the rank structure found in the filtered back-projection formula. As a result, empirically, our framework is able to provide sharp reconstructions effortlessly, even recovering sub-Nyquist features in the multiple-scattering regime. It has low-sample and computational complexity, its number of parameters scales sub-linearly with the target resolution, and it has stable training dynamics.

翻译：我们提出《宽带反向投影扩散》，一种用于从宽带散射数据近似逆散射映射所诱导的后验分布的端到端概率框架。该框架利用条件扩散模型，结合波传播的基本物理原理及问题中的对称性，以生成高精度重建结果。该框架将得分函数分解为：受滤波反向投影公式启发的基于物理的潜在表示，以及以该潜在表示为条件的条件得分函数。这两个步骤在公式中被约束为服从对称性，同时通过施加滤波反向投影公式中存在的秩结构，可实现压缩。因此，经验表明，我们的框架能够轻松提供清晰的重建结果，甚至能在多重散射机制中恢复亚奈奎斯特特征。该框架具有较低的样本和计算复杂度，其参数数量随目标分辨率呈次线性增长，且训练动态稳定。