通过主成分正则化，提升生成模型对图像后验分布的准确采样能力。
pcaGAN: Improving Posterior-Sampling cGANs via Principal Component Regularization
- 引入主成分正则化，精准控制后验均值与协方差结构。
- 在去噪、大尺度补全和加速MRI重建中优于现有cGAN与扩散模型。
- 适合需要高精度不确定性建模的医学成像与逆问题求解场景。
在病态成像逆问题中，可能存在多个同时符合观测数据和先验知识的图像假设。传统方法仅返回一个假设，而后验采样器通过生成多个可能的假设来探索整个解空间，可用于量化不确定性或构建兼顾感知质量与失真权衡的恢复结果。本文提出一种快速且精确的后验采样条件生成对抗网络（cGAN），通过新型正则化方式，使后验均值以及后验协方差矩阵的迹和前K个主成分保持正确。数值实验表明，该方法在去噪、大尺度图像补全及加速MRI恢复等任务中，优于当前主流的cGAN与扩散模型。代码见：https://github.com/matt-bendel/pcaGAN。
原文摘要 · Abstract (English)
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.
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