Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees
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.
Code (1)
Tasks
Compressive SensingGenerative Adversarial NetworkMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Provably Convergent Algorithms for Solving Inverse Problems Using Generative Models
The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this w…
Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restri…
DecoderGaussian Process Regression for Inverse Problems in Linear PDEs
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian process…
Computational EfficiencyGaussian ProcessesregressionSolving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo
A recent line of research has exploited pre-trained generative diffusion models as priors for solving Bayesian inverse problems. We contribute to this research direction by designing a sequential Monte Carlo method for l…
Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors
Deep neural networks as image priors have been recently introduced for problems such as denoising, super-resolution and inpainting with promising performance gains over hand-crafted image priors such as sparsity and low-…
Compressive SensingDenoisingRetrievalSuper-Resolution