DeepGEM: Generalized Expectation-Maximization for Blind Inversion
DeepGEM: Generalized Expectation-Maximization for Blind Inversion
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发表时间：
2021
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通讯作者：
Angela F. Gao;J. Castellanos;Yisong Yue;Z. Ross;K. Bouman
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作者：
Angela F. Gao;J. Castellanos;Yisong Yue;Z. Ross;K. Bouman
通常，反演算法假设正演模型是已知和固定的，正演模型将源与其结果测量相关联。利用收集到的间接测量数据和正演模型，目标变为恢复源。当前向模型未知或不完美时，由于模型不匹配而导致的工件会在源的恢复中出现。本文研究了盲反演问题：求解未知或不完全正演模型参数的反演问题。我们提出了DeepGEM，一个变分期望最大化（EM）框架，可用于以无监督的方式求解前向模型的未知参数。DeepGEM利用归一化流生成网络来有效捕获复杂的后验分布，从而更准确地评估EM中使用的震源后验分布。我们通过在盲地震层析成像这一具有挑战性的问题上取得出色的表现，展示了DeepGEM方法的有效性，在这一问题上，我们显著优于地震学中使用的标准方法。我们还通过将DeepGEM应用于一个简单的盲反卷积案例来证明它的普遍性。在联合地震层析成像和震源定位任务中取得了出色的表现，大大优于目前在地震学合成数据中使用的标准方法。所提出的框架是灵活的，可以应用于需要估计或微调前向模型参数的不同应用。我们还通过将该方法应用于一个简单但具有挑战性的盲反卷积问题来证明这种灵活性。未来的工作包括将该方法应用于实际地震数据，扩展到其他应用，并结合数据驱动的先验。我们的研究结果强调了将物理健全的基于模型的技术与盲逆问题的学习机制相结合的好处。
Typically, inversion algorithms assume that a forward model, which relates a source to its resulting measurements, is known and fixed. Using collected indirect measurements and the forward model, the goal becomes to recover the source. When the forward model is unknown, or imperfect, artifacts due to model mismatch occur in the recovery of the source. In this paper, we study the problem of blind inversion: solving an inverse problem with unknown or imperfect knowledge of the forward model parameters. We propose DeepGEM, a variational Expectation-Maximization (EM) framework that can be used to solve for the unknown parameters of the forward model in an unsupervised manner. DeepGEM makes use of a normalizing flow generative network to efficiently capture complex posterior distributions, which leads to more accurate evaluation of the source’s posterior distribution used in EM. We showcase the effectiveness of our DeepGEM approach by achieving strong performance on the challenging problem of blind seismic tomography, where we significantly outperform the standard method used in seismology. We also demonstrate the generality of DeepGEM by applying it to a simple case of blind deconvolution. achieves strong performance in the task of joint seismic tomography and earthquake source localization, substantially outperforming standard approaches currently being used in seismology on synthetic data. The proposed framework is flexible and can be applied to different applications that require estimation or fine tuning of forward model parameters. We demonstrate this flexibility by also applying the approach to a simple, but challenging, blind deconvolution problem. Future work includes applying this method to real seismic data, extending to other applications, and incorporating data-driven priors. Our results highlight the benefit of blending physically sound model-based techniques with learning machinery for blind inverse problems.