A Regularized Conditional GAN for Posterior Sampling in Image Recovery Problems

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 Fréchet 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.