用成对自编码器建模隐空间，解决观测不一致下的反问题重建。
Latent Space Inference via Paired Autoencoders
- 通过参数与观测空间的成对自编码器，建立隐空间映射关系。
- 在数据不完整或含噪时，重构精度优于传统端到端模型。
- 适用于医学断层成像和地震波反演等科学工程反问题。
本文提出一种基于成对自编码器的数据驱动隐空间推断框架，用于处理求解反问题时的观测不一致性。该方法使用两个自编码器，分别对应参数空间和观测空间，并通过学习隐空间之间的映射关系实现连接。这些映射提供了一种低维、信息丰富的代理正则化反演与优化方案。所提框架可处理部分、噪声或分布外数据，同时保持与底层物理模型的一致性。成对自编码器能先重建受损数据，再利用重建结果进行参数估计，相比仅使用成对自编码器或同架构的端到端编码器，在数据不一致场景下表现更优。我们在医学断层成像和地球物理地震波形反演两个成像案例中验证了该方法的有效性，但其适用范围可推广至多种科学与工程领域的反问题。
原文摘要 · Abstract (English)
This work describes a novel data-driven latent space inference framework built on paired autoencoders to handle observational inconsistencies when solving inverse problems. Our approach uses two autoencoders, one for the parameter space and one for the observation space, connected by learned mappings between the autoencoders' latent spaces. These mappings enable a surrogate for regularized inversion and optimization in low-dimensional, informative latent spaces. Our flexible framework can work with partial, noisy, or out-of-distribution data, all while maintaining consistency with the underlying physical models. The paired autoencoders enable reconstruction of corrupted data, and then use the reconstructed data for parameter estimation, which produces more accurate reconstructions compared to paired autoencoders alone and end-to-end encoder-decoders of the same architecture, especially in scenarios with data inconsistencies. We demonstrate our approaches on two imaging examples in medical tomography and geophysical seismic-waveform inversion, but the described approaches are broadly applicable to a variety of inverse problems in scientific and engineering applications.
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