"Provably Accurate, Stable and Efficient Deep Neural Networks for Compressive Imaging"
Neyra-Nesterenko, MaksymDeep learning has recently shown substantial potential to outperform standard methods in compressive imaging, that is, image reconstruction using highly undersampled measurements. Given compressive imaging arises in many important applications, such as medical imaging, the potential impact of deep learning is significant. Empirical results indicate deep learning achieves superior accuracy on data for such tasks. However, a theoretical treatment ensuring the stability of deep learning for compressive imaging is mostly absent in the current literature. In fact, many existing deep neural networks designed for these tasks are unstable and fail to generalize. In this work, we present a novel construction of accurate, stable and efficient neural networks for gradient-based compressive imaging. This is based on recent work by Adcock et al. (2021) and Antun et al. (2021). We use unravelling, a technique used to construct networks from optimization algorithm iterates. We utilize a compressed sensing analysis to prove accuracy and stability of the network. Using a restart scheme, we enable exponential decay in the required network depth, yielding a shallower network. In turn this reduces computational costs, making the network feasible for fast image reconstruction. This is joint work with Ben Adcock.