Intelligent priors for high-precision imaging inverse problems

Plug-and-Play (PnP) algorithms are widely used in inverse imaging tasks due to their interpretability, scalability, and generalizability. By substituting hand-crafted priors in optimization algorithms with denoisers, PnP methods allow us to leverage both optimization techniques through data fidelity terms and learned deep neural networks as prior operators. Although Gaussian denoisers have shown superior performance in various imaging applications, recent studies indicate that deep networks trained for more general restoration tasks can yield more promising results. This thesis aims to explore priors that are more intelligent than simple denoisers for regularizing inverse problems to develop precise and scalable computational imaging techniques for astronomical and medical imaging applications. Additionally, this research will examine the theoretical aspects of the algorithms to ensure that the proposed methods are well-defined.