Abhilash Nandy, Yash Agarwal, Ashish Patwa, Millon Madhur Das, Aman Bansal, Ankit Raj, Pawan Goyal, Niloy Ganguly. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing. 2024.

Deep-learning-based methods for various applications have been shown vulnerable to adversarial examples. Here we address the use of deep-learning networks as inverse problem solvers, which has generated much excitement and even adoption efforts by the main equipment vendors for medical imaging including computed tomography (CT) and MRI. However, the recent demonstration that such networks suffer from a similar vulnerability to adversarial attacks potentially undermines their future. We propose to modify the training strategy of end-to-end deep-learning-based inverse problem solvers to improve robustness. To this end, we introduce an auxiliary net-work to generate adversarial examples, which is used in a min-max formulation to build robust image reconstruction networks. Theoretically, we argue that for such inverse problem solvers, one should analyze and study the effect of adversaries in the measurement-space, instead of in the signal-space used in previous work. We show for a linear reconstruction scheme that our min-max formulation results in a singular-value filter regularized solution, which suppresses the effect of adversarial examples. Numerical experiments using the proposed min-max scheme confirm convergence to this solution. We complement the theory by experiments on non-linear Compressive Sensing(CS) reconstruction by a deep neural network on two standard datasets, and, using anonymized clinical data, on a state-of-the-art published algorithm for low-dose x-ray CT reconstruction. We show a significant improvement in robustness over other methods for deep network-based reconstruction, by using the proposed approach.

A Generative Adversarial Network (GAN) with generator G trained to model the prior of images has been shown to perform better than sparsity-based regularizers in ill-posed inverse problems. Here, we propose a new method of deploying a GAN-based prior to solve linear inverse problems using projected gradient descent (PGD). Our method learns a network-based projector for use in the PGD algorithm, eliminating expensive computation of the Jacobian of G. Experiments show that our approach provides a speed-up of 60-80x over earlier GAN-based recovery methods along with better accuracy in compressed sensing. Our main theoretical result is that if the measurement matrix is moderately conditioned on the manifold range(G) and the projector is \delta-approximate, then the algorithm is guaranteed to reach O(\delta) reconstruction error in O(log(1/\delta)) steps in the low noise regime. Additionally, we propose a fast method to design such measurement matrices for a given G. Extensive experiments demonstrate the efficacy of this method by requiring 5-10x fewer measurements than random Gaussian measurement matrices for comparable recovery performance. Because the learning of the GAN and projector is decoupled from the measurement operator, our GAN-based projector and recovery algorithm are applicable without retraining to all linear inverse problems in which the measurement operator is moderately conditioned for range(G), as confirmed by experiments on compressed sensing, super-resolution, and inpainting.