GAN-based Projector for Faster Recovery in Compressed Sensing with Convergence Guarantees

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GAN-based Projector for Faster Recovery in Compressed Sensing with Convergence Guarantees by Ankit Raj, Yuqi Li, Yoram Bresler

A Generative Adversarial Network (GAN) with generator G trained to model the prior of images has been shown to perform better than sparsity-based regularizers in ill-posed inverse problems. In this work, we propose a new method of deploying a GAN-based prior to solve linear inverse problems using projected gradient descent (PGD). Our method learns a network-based projector for use in the PGD algorithm, eliminating the need for expensive computation of the Jacobian of G. Experiments show that our approach provides a speed-up of 30-40× over earlier GAN-based recovery methods for similar accuracy in compressed sensing. Our main theoretical result is that if the measurement matrix is moderately conditioned for range(G) and the projector is δ-approximate, then the algorithm is guaranteed to reach O(δ) reconstruction error in O(log(1/δ)) steps in the low noise regime. Additionally, we propose a fast method to design such measurement matrices for a given G. Extensive experiments demonstrate the efficacy of this method by requiring 5-10× fewer measurements than random Gaussian measurement matrices for comparable recovery performance.

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