Invertible generative models for inverse problems: mitigating representation error and dataset bias
Invertible generative models for inverse problems: mitigating representation error and dataset bias
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发表时间：
2019-05
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通讯作者：
Muhammad Asim;Ali Ahmed;Paul Hand
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作者：
Muhammad Asim;Ali Ahmed;Paul Hand
经过训练的生成模型在成像逆问题的先验中表现出了卓越的性能——例如，生成对抗网络先验允许从比稀疏先验少5-10倍的测量中恢复测试图像。不幸的是，由于架构选择、模式崩溃和训练数据集中的偏差，这些模型可能无法表示任何特定的图像。在本文中，我们证明了可逆神经网络，其设计具有零表示误差，可以作为有效的自然信号先验在逆问题，如去噪，压缩感知和油漆。给定一个训练好的生成模型，我们研究了在正则化下期望逆问题的经验风险公式，该正则化可以直接通过惩罚或算法通过初始化来提升高似然图像。对于压缩感知，在几乎所有欠采样比率下，可逆先验比稀疏先验产生更高的精度，并且由于它们缺乏表示误差，对于在有偏差的训练集中具有罕见变化特征的图像，包括分布外的自然图像，可逆先验可以比GAN先验产生更好的重建。我们还比较了压缩感知与非学习方法（如深度解码器）的性能，并在线性可逆模型的情况下建立了预期恢复误差的理论界限。
Trained generative models have shown remarkable performance as priors for inverse problems in imaging -- for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training dataset. In this paper, we demonstrate that invertible neural networks, which have zero representation error by design, can be effective natural signal priors at inverse problems such as denoising, compressive sensing, and inpainting. Given a trained generative model, we study the empirical risk formulation of the desired inverse problem under a regularization that promotes high likelihood images, either directly by penalization or algorithmically by initialization. For compressive sensing, invertible priors can yield higher accuracy than sparsity priors across almost all undersampling ratios, and due to their lack of representation error, invertible priors can yield better reconstructions than GAN priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images. We additionally compare performance for compressive sensing to unlearned methods, such as the deep decoder, and we establish theoretical bounds on expected recovery error in the case of a linear invertible model.