标题： pcaGAN：通过主成分正则化改进后验采样的条件生成对抗网络 显示英文标题

标题： pcaGAN: Improving Posterior-Sampling cGANs via Principal Component Regularization

摘要： 在不适定的成像反问题中，可能存在许多假设既符合观测到的测量值，又符合真实图像的先验知识。后验采样器的目标不是仅仅返回该图像的一个假设，而是通过生成许多可能的假设来探索完整的解空间，这些假设之后可用于量化不确定性或构建能够适当权衡感知/失真折中的恢复方法。 在这项工作中，我们提出了一种快速且准确的后验采样条件生成对抗网络（cGAN），它通过一种新颖的正则化形式，旨在使后验均值以及后验协方差矩阵的迹和K个主成分的正确性得以实现。数值实验表明，我们的方法在去噪、大规模修复和加速MRI恢复等成像反问题上优于当代cGAN和扩散模型。我们的模型代码可以在以下地址找到：https://github.com/matt-bendel/pcaGAN。 显示英文摘要

摘要： In ill-posed imaging inverse problems, there can exist many hypotheses that fit both the observed measurements and prior knowledge of the true image. Rather than returning just one hypothesis of that image, posterior samplers aim to explore the full solution space by generating many probable hypotheses, which can later be used to quantify uncertainty or construct recoveries that appropriately navigate the perception/distortion trade-off. In this work, we propose a fast and accurate posterior-sampling conditional generative adversarial network (cGAN) that, through a novel form of regularization, aims for correctness in the posterior mean as well as the trace and K principal components of the posterior covariance matrix. Numerical experiments demonstrate that our method outperforms contemporary cGANs and diffusion models in imaging inverse problems like denoising, large-scale inpainting, and accelerated MRI recovery. The code for our model can be found here: https://github.com/matt-bendel/pcaGAN.