Abstract
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. For the same accuracy on test images, they can use 10-20x fewer measurements. We demonstrate that invertible priors can yield better reconstructions than sparsity priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images.
Abstract (translated)
经过训练的生成模型作为成像逆问题的先验，表现出显著的性能。例如，生成对抗网络优先级允许从比稀疏优先级少5-10倍的测量值恢复测试图像。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。本文证明了设计误差为零的可逆神经网络在去噪、压缩传感和修复等逆问题上是有效的自然信号先验。在一个有训练的生成模型下，我们研究了在正则化下期望逆问题的经验风险公式，这种规则化可以直接通过惩罚或通过初始化算法来提升高似然图像。对于压缩传感，在几乎所有的欠采样率下，可逆先验比稀疏先验能产生更高的精度。对于相同精度的测试图像，他们可以使用10-20倍较少的测量。我们证明了对于具有偏差训练集内罕见变异特征的图像（包括分布外的自然图像），可逆先验比稀疏先验能产生更好的重建效果。
URL
https://arxiv.org/abs/1905.11672
