In image recovery problems, one seeks to infer an image from distorted, incomplete, and/or noise-corrupted measurements. Such problems arise in magnetic resonance imaging (MRI), computed tomography, deblurring, super-resolution, inpainting, phase retrieval, image-to-image translation, and other applications. Given a training set of signal/measurement pairs, we seek to do more than just produce one good image estimate. Rather, we aim to rapidly and accurately sample from the posterior distribution. To do this, we propose a regularized conditional Wasserstein GAN that generates dozens of high-quality posterior samples per second. Our regularization comprises an $\ell_1$ penalty and an adaptively weighted standard-deviation reward. Using quantitative evaluation metrics like conditional Fr\'{e}chet inception distance, we demonstrate that our method produces state-of-the-art posterior samples in both multicoil MRI and large-scale inpainting applications. The code for our model can be found here: https://github.com/matt-bendel/rcGAN

翻译：在图像恢复问题中，目标是从畸变、不完整和/或受噪声污染的测量中推断出图像。此类问题出现在磁共振成像、计算机断层扫描、去模糊、超分辨率、图像修复、相位恢复、图像到图像翻译及其他应用中。给定信号/测量对的训练集，我们不仅要生成单个优质图像估计，更要快速准确地从后验分布中进行采样。为此，我们提出一种正则化条件Wasserstein生成对抗网络，该网络每秒可生成数十个高质量后验样本。我们的正则化方法包含$\ell_1$惩罚项和自适应加权标准差奖励项。通过条件弗雷歇初始距离等定量评估指标，我们证明该方法在多线圈磁共振成像和大规模图像修复应用中均能产生当前最先进的后验样本。本模型的代码可访问以下链接获取：https://github.com/matt-bendel/rcGAN