Generative models and robustness in deep learning for inverse problems
Image reconstruction comprises several real-life applications such as super-resolution and in painting as well as critical medical imaging problems like CT and MRI. Deep learning based methods have recently been demonstrated to achieve state-of-the-art results on such tasks. In this thesis, we address two important aspects related to deep-learning-based image reconstruction – (i) architecture design and guarantees, and (ii) robustness and stability. To address the first aspect, we propose (joint work with Yuqi Li) a new method of deploying a GAN-based prior to solve linear inverse problems using projected gradient descent (PGD). Experiments show that our approach provides a speed-up of 60-80× over earlier GAN-based recovery methods along with better accuracy. Our main theoretical result is that if the measurement matrix is moderately conditioned on the manifold range R(G) and the projector is δ-approximate, then the algorithm is guaranteed to reach O(δ) recovery error in O(log(1/δ)) steps in low noise regime. Secondly, we argue that for inverse problem solvers, one should analyze and study the effect of adversaries and robustness in the measurement-space, instead of formulating in the signal-space as in previous work. We propose to introduce an auxiliary network to generate adversarial examples, which is used in a min-max formulation to build robust image reconstruction networks. Theoretically, we show for a linear reconstruction scheme the min-max formulation results in a singular-value(s) filter regularized solution, which suppresses the effect of adversarial examples occurring because of ill-conditioning in the measurement matrix. Furthermore, we propose to use the idea of interval-bound propagation to minimize an upper bound on the reconstruction loss, given the perturbation. We show that it is computationally more efficient and gives slightly better performance in terms of robustness than the adversarial training based method that we proposed.
Image Reconstruction, Adversarial Training
University of Illinois - Urbana-Champaign
Networked Digital Library of Theses and Dissertations
University of Illinois at Urbana-Champaign