Inverse problems are fundamental to many scientific and engineering disciplines; they arise when one seeks to reconstruct hidden, underlying quantities from noisy measurements. Many applications demand not just point estimates but interpretable uncertainty. Providing fast inference alongside uncertainty estimates remains challenging yet desirable in numerous applications. We propose the Variational Sparse Paired Autoencoder (vsPAIR) to address this challenge. The architecture pairs a standard VAE encoding observations with a sparse VAE encoding quantities of interest, connected through a learned latent mapping. The variational structure enables uncertainty estimation, the paired architecture encourages interpretability by anchoring QoI representations to clean data, and sparse encodings provide structure by concentrating information into identifiable factors rather than diffusing across all dimensions. To validate the effectiveness of our proposed architecture, we conduct experiments on blind inpainting and computed tomography, demonstrating that vsPAIR is a capable inverse problem solver that can provide interpretable and structured uncertainty estimates.

翻译：反问题是众多科学与工程领域的核心问题，其目标是从含噪声的观测数据中重建隐藏的底层物理量。许多应用不仅需要点估计，更要求可解释的不确定性。在大量实际场景中，实现快速推断并同时提供不确定性估计仍具挑战性但备受期待。为此，我们提出了变分稀疏配对自编码器（vsPAIR）以应对这一挑战。该架构将编码观测数据的标准变分自编码器（VAE）与编码目标物理量的稀疏VAE相配对，二者通过习得的隐空间映射相连接。其变分结构支持不确定性估计，配对架构通过将目标物理量表示锚定于干净数据以提升可解释性，而稀疏编码则通过将信息集中于可识别的隐变量而非分散至所有维度来提供结构化表征。为验证所提架构的有效性，我们在盲修复与计算机断层成像任务上进行了实验，结果表明vsPAIR能够作为有效的反问题求解器，提供可解释且结构化的不确定性估计。