Computational imaging problems are traditionally formulated as ill-posed inverse problems, where prior knowledge is essential for recovering high-quality images from limited or corrupted measurements. Classical approaches rely on explicitly defined priors, leading to optimization problems that are mathematically principled but often limited in their ability to capture the complexity of real-world data.
In this talk, I will argue that recent advances in generative modeling are driving a fundamental shift: from explicit priors to learned restoration operators that implicitly encode data distributions. Rather than specifying a prior as a function, we now access it through learned models that can be queried but not explicitly written down. This perspective reframes inverse problems as the design of iterative algorithms that interact with these operators.
I will present an optimization-centric view that connects classical proximal methods, plug-and-play algorithms, and modern generative models within this operator-centric framework. I will highlight three key ideas: (i) general restoration operators implicitly define priors, (ii) stochasticity can be used as a principled tool to improve optimization behavior in highly ill-posed problems, and (iii) priors can be learned directly from measurements without access to clean training data. The talk will cover both the theoretical foundations of these ideas and their applications in biomedical image reconstruction.
