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.