pcaGAN: Improving Posterior-Sampling cGANs via Principal Component Regularization
This work addresses uncertainty quantification and recovery quality in imaging inverse problems for applications such as medical imaging, though it appears incremental as it builds on existing cGAN methods with a novel regularization approach.
The paper tackles ill-posed imaging inverse problems by proposing pcaGAN, a fast and accurate posterior-sampling cGAN that improves correctness in posterior mean and covariance components, outperforming contemporary cGANs and diffusion models in tasks like denoising, inpainting, and MRI recovery.
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.