Deep Model-Based Architectures for Inverse Problems Under Mismatched Priors
Deep Model-Based Architectures for Inverse Problems Under Mismatched Priors
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DOI：
10.1109/jsait.2022.3220044
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
S. Shoushtari;Jiaming Liu;Yuyang Hu;U. Kamilov
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文献类型：
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作者：
S. Shoushtari;Jiaming Liu;Yuyang Hu;U. Kamilov
人们对基于深度模型的架构（DMBA）越来越感兴趣，该架构通过将物理测量模型与使用卷积神经网络（CNN）指定的学习图像先验相结合来解决成像逆问题。例如，用于系统地设计DMBA的公知框架包括即插即用先验（Plug-and-Play Priors，PMBA）、深度展开（Deep Unfolding，DU）和深度均衡模型（Deep Equilibrium Model，DEQ）。虽然DMBA的经验性能和理论特性已经得到了广泛的研究，在该领域的现有工作主要集中在他们的性能时，所需的图像先验是确切知道的。这项工作通过在不匹配的CNN先验下对DMBA提供新的理论和数值见解来解决先前工作中的差距。当训练数据和测试数据之间存在分布偏移时，自然会出现不匹配的先验，例如，由于测试图像来自与用于训练CNN先验的图像不同的分布。当用于推断的CNN先验是某些期望的统计估计量（MAP或MMSE）的近似值时，也会出现这种情况。我们的理论分析在一组明确指定的假设下，由于不匹配的CNN先验，提供了解决方案的明确误差范围。我们的数值结果比较DMBA的经验表现下现实的分布变化和近似的统计估计。
There is a growing interest in deep model-based architectures (DMBAs) for solving imaging inverse problems by combining physical measurement models and learned image priors specified using convolutional neural nets (CNNs). For example, well-known frameworks for systematically designing DMBAs include plug-and-play priors (PnP), deep unfolding (DU), and deep equilibrium models (DEQ). While the empirical performance and theoretical properties of DMBAs have been widely investigated, the existing work in the area has primarily focused on their performance when the desired image prior is known exactly. This work addresses the gap in the prior work by providing new theoretical and numerical insights into DMBAs under mismatched CNN priors. Mismatched priors arise naturally when there is a distribution shift between training and testing data, for example, due to test images being from a different distribution than images used for training the CNN prior. They also arise when the CNN prior used for inference is an approximation of some desired statistical estimator (MAP or MMSE). Our theoretical analysis provides explicit error bounds on the solution due to the mismatched CNN priors under a set of clearly specified assumptions. Our numerical results compare the empirical performance of DMBAs under realistic distribution shifts and approximate statistical estimators.