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A Generative Adversarial Network (GAN) with generator $G$ trained to modelthe prior of images has been shown to perform better than sparsity-basedregularizers in ill-posed inverse problems. Here, we propose a new method ofdeploying a GAN-based prior to solve linear inverse problems using projectedgradient descent (PGD). Our method learns a network-based projector for use inthe PGD algorithm, eliminating expensive computation of the Jacobian of $G$.Experiments show that our approach provides a speed-up of $60\text{-}80\times$over earlier GAN-based recovery methods along with better accuracy. Our maintheoretical result is that if the measurement matrix is moderately conditionedon the manifold range($G$) and the projector is $\delta$-approximate, then thealgorithm is guaranteed to reach $O(\delta)$ reconstruction error in$O(log(1/\delta))$ steps in the low noise regime. Additionally, we propose afast method to design such measurement matrices for a given $G$. Extensiveexperiments demonstrate the efficacy of this method by requiring$5\text{-}10\times$ fewer measurements than random Gaussian measurementmatrices for comparable recovery performance. Because the learning of the GANand projector is decoupled from the measurement operator, our GAN-basedprojector and recovery algorithm are applicable without retraining to alllinear inverse problems, as confirmed by experiments on compressed sensing,super-resolution, and inpainting.

GAN-based Projector for Faster Recovery with Convergence Guarantees in Linear Inverse Problems