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

By Viraj Shah, Chinmay Hegde. 2018

183 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Generative Models, Numerical Methods & Scientific Computing

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Citations in the corpus

An overview of deep learning in medical imaging focusing on MRI (2018, background): “(30)See [154, 155, 156, 157, 158] for recent perspectives and developments connecting deep learning-based reconstruction methods to the more general research field of inverse problems.”
Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser (2020, background): “Generative Adversarial Networks (GANs) [9] have been shown capable of synthesizing novel high-quality images, that may be viewed as samples of an implicit prior density model, and recent methods have been developed to use these priors in solving inverse problems [10, 11].”
Transforming and Projecting Images into Class-conditional Generative Networks (2020, methodology): “, ADAM, LBFGS) [70, 12, 46, 66, 57, 3, 13] or MCMC [61], (2) Encoder-based methods: they learn an encoder to directly predict the latent vector given a real image [15, 19, 70, 53, 12, 16], (3) Hybrid methods [70, 8, 10]: they use the encoder to initialize the latent vector and then solve the optimiz”
Deep Learning Techniques for Inverse Problems in Imaging (2020, methodology): “given by [137], while ADMM methods were proposed and analyzed in [138].”
Image-Adaptive GAN based Reconstruction (2019, unknown): “This shortcoming is mainly due to the limited representation capabilities of the generative models (see Section 6.3 in (Bora et al. 2017)), and is common to related recent works (Hand, Leong, and Voroninski 2018; Bora, Price, and Dimakis 2018; Dhar, Grover, and Ermon 2018; Shah and Hegde 2018).”
Inverting Deep Generative models, One layer at a time (2019, methodology): “[24] provide theoretical guarantees on obtaining the optimal solution for (2) with projected gradient descent, provided one could solve (1) exactly.”
GAN-Based Projector for Faster Recovery With Convergence Guarantees in Linear Inverse Problems (2019, methodology): “To resolve this problem, Shah and Hegde [33] proposed a projected gradient descent (PGD)-based method (which we call PGD-GAN) to solve (2), shown in fig.2(a).”
When and How Can Deep Generative Models be Inverted? (2020, background): “A close but diﬀerent line of theoretical work analyze the compressive sensing abilities of trained deep generative networks [22, 5].”
MimicGAN: Robust Projection onto Image Manifolds with Corruption Mimicking (2019, methodology): “This is commonly adopted in several stateof-the-art solutions for image inpainting [58], adversarial defense [48], compressed sensing [13],[53], and deblurring [8].”