In inverse problems, one seeks to reconstruct an image from incomplete and/or degraded measurements. Such problems arise in magnetic resonance imaging (MRI), computed tomography, deblurring, superresolution, inpainting, and other applications. It is often the case that many image hypotheses are consistent with both the measurements and prior information, and so the goal is not to recover a single ``best'' hypothesis but rather to explore the space of probable hypotheses, i.e., to sample from the posterior distribution. In this work, we propose a regularized conditional Wasserstein GAN that can generate dozens of high-quality posterior samples per second. 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 inpainting applications.
翻译:反面问题,人们试图从不完整和/或退化的测量中重建图像,这些问题出现在磁共振成像(MRI)、计算成的断层成像、分流、超分辨率、油漆和其他应用中,许多图像假设往往与测量和先前信息相一致,因此,目标不是要恢复一个单一的“最佳”假设,而是要探索可能的假设空间,即从后方分布到样本。在这项工作中,我们建议采用固定条件的瓦瑟斯坦GAN,每秒可产生几十个高品质的远层样品。我们使用像条件性Fr\'{e}切切特初始距离这样的定量评估指标,我们证明我们的方法在多石油 MRI 和 油漆应用中产生最先进的远端样品。