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 , 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 , 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 , 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
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