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.

中文翻译：

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反向投影扩散：使用扩散模型求解宽带逆散射问题

我们提出了宽带反向投影扩散，这是一个端到端的概率框架，用于近似由宽带散射数据中的逆散射图引起的后验分布。该框架产生高度精确的重建，利用条件扩散模型来绘制样本，并且还尊重波传播基础物理学的对称性。该过程分为两个步骤：第一步，受过滤后的反向传播公式的启发，将数据转换为基于物理的潜在表示，而第二步学习以该潜在表示为条件的条件评分函数。这两个步骤单独遵循其关联的对称性，并且可以通过施加过滤的反向投影公式中的 rank 结构来进行压缩。从经验上讲，我们的框架具有较低的样本和计算复杂性，其参数数量仅随目标分辨率呈亚线性缩放，并且具有稳定的训练动力学。它毫不费力地提供清晰的重建，甚至能够在多重散射状态下恢复亚奈奎斯特特征。