# Solving inverse problems using GAN priors

In recent works, both sparsity-based methods as well as learningbased
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.
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 generative adversarial networks, or GANs). On this lines, we advocate the idea of replacing hand-crafted priors,
such as sparsity, with a generative model such as Generative Adversarial Network (GAN)
to solve linear inverse problems such as compressive sensing.
We leveraged the ability of Generative Adversarial Networks (GAN) of learning the real data distribution by using the generator
function as a prior on natural images to solve ill-posed inverse problems such as compressive sensing and phase retrieval.

In our first work [1], 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.

In [2], we study the algorithmic aspects of such a learning based
approach from a theoretical perspective. For certain generative network architectures, we establish a simple nonconvex
algorithmic approach that (a) theoretically enjoys linear
convergence guarantees for certain inverse problems, and
(b) empirically improves upon conventional techniques such
as back-propagation.

In [3], propose two algorithms to solve the phase retrieval problem. Our proposed algorithms
combine the ideas from AltMin approach for non-convex sparse phase
retrieval and projected gradient descent approach for solving linear
inverse problems using generative priors.

Publications
1. V. Shah and C. Hegde, Solving linear inverse problems using GAN priors: an algorithm with provable guarantees, ICASSP, 2018. . [Paper / Poster / Code

]

2. C. Hegde, Algorithmic Aspects of Inverse Problems Using Generative Models, Allerton Conference on Communication, Control, and Computing, October 2018. [Paper

]

3. R. Hyder, V. Shah, C. Hegde, and S. Asif, Alternating Phase Projected Gradient Descent With Generative Priors for Compressive Phase Retrieval, ICASSP, May 2019. [Paper

]

## People

Assistant Professor, ECPE