A Regularized Conditional GAN for Posterior Sampling in Image Recovery Problems

Matthew Bendel, Rizwan Ahmad, Philip Schniter

In image recovery problems, one seeks to reconstruct 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 design a method to generate posterior samples rapidly and accurately. In particular, 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 Fr\'{e}chet inception distance, we demonstrate that our method produces state-of-the-art posterior samples in both multicoil MRI and large-scale inpainting applications.

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