Learning Provably Robust Estimators for Inverse Problems via Jittering.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computer Vision

Background:

• Deep neural networks excel at inverse problems but are vulnerable to worst-case perturbations.
• The robustness of these networks, especially for inverse problems, remains a critical research question.

Purpose of the Study:

• To investigate the effectiveness of jittering, a regularization technique, for training worst-case robust deep neural networks for inverse problems.
• To analytically characterize optimal worst-case robust estimators for linear denoising and evaluate jittering's performance.

Main Methods:

• Analytical characterization of optimal $\ell_2$-worst-case robust estimators for linear denoising.
• Empirical evaluation of jittering using deep neural networks (U-nets) for image denoising, deconvolution, and accelerated MRI.

Main Results:

• Jittering yields optimal robust denoisers for linear denoising tasks.
• Empirical results show jittering significantly improves worst-case robustness in image denoising, deconvolution, and MRI.
• Jittering can be suboptimal for inverse problems beyond simple denoising.

Conclusions:

• Jittering is an effective method for enhancing worst-case robustness in deep learning for inverse problems, particularly denoising.
• Training on naturally noisy data offers some degree of robustness enhancement.
• Further research is needed to optimize jittering for complex inverse problems.