Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees

2018/02/23 by Viraj Shah, Chinmay Hegde, Shah, Viraj +1 · 9 citations
Computer Science · Engineering · Mathematics · #Advanced Image Processing Techniques #FOS: Computer and information sciences #Image and Signal Denoising Methods #Indoor and Outdoor Localization Technologies #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1802.08406

arxiv created 2018/02/23 · openalex publication_date 2018/02/23 · arxiv updated 2018/02/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In recent works, both sparsity-based methods as well as learning-based methods have proven to be successful in solving several challenging linear inverse problems. However, sparsity priors for natural signals and images suffer from poor discriminative capability, while learning-based methods seldom provide concrete theoretical guarantees. In this work, we advocate the idea of replacing hand-crafted priors, such as sparsity, with a Generative Adversarial Network (GAN) to solve linear inverse problems such as compressive sensing. In particular, we propose a projected gradient descent (PGD) algorithm for effective use of GAN priors for linear inverse problems, and also provide theoretical guarantees on the rate of convergence of this algorithm. Moreover, we show empirically that our algorithm demonstrates superior performance over an existing method of leveraging GANs for compressive sensing.

Citations

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Cited by

• DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing
• Solving Inverse Problems with FLAIR
• Inverting Deep Generative models, One layer at a time
• Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models
• Learning Single Index Models with Diffusion Priors
• Projection-Based Correction for Enhancing Deep Inverse Networks
• Stochastic Orthogonal Regularization for deep projective priors
• How many measurements are enough? Bayesian recovery in inverse problems with general distributions
• Provably Convergent Algorithms for Solving Inverse Problems Using Generative Models

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• Invertible generative models for inverse problems: mitigating representation error and dataset bias