NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems

Understand

Solving inverse problems is a fundamental component of science, engineering and mathematics.

• With the advent of deep learning, deep neural networks have significant potential to outperform existing state-of-the-art, model-based methods for solving inverse problems.
• However, it is known that current data-driven approaches face several key issues, notably hallucinations, instabilities and unpredictable generalization, with potential impact in critical tasks such as medical imaging.
• This raises the key question of whether or not one can construct deep neural networks for inverse problems with explicit stability and accuracy guarantees.