ABSTRACT

Solving inverse problems remains a fundamental challenge in computational imaging, often requiring large datasets, carefully tuned regularisation, or extensive supervision. Yet in many real-world scenarios, such resources are unavailable — we may only have a single noisy observation and no access to similar examples. In this talk, we will discuss how we can still meaningfully approach inverse problems under such constraints, by leveraging single-instance priors — structural biases learned from the data point itself.

We will explore the limitations of conventional deep learning pipelines, including their dependence on large-scale training and vulnerability to overfitting in low-data regimes. Then, we will introduce a line of recent work showing that, with the right optimisation and structural strategies, one can build single-instance priors — enabling stable and effective reconstructions even in severely underdetermined settings. This talk will walk through our journey in rethinking priors: moving from generic plug-and-play formulations to formulations that exploit both spatial and frequency structures in data. The results offer not only practical solutions for data-scarce settings, but also new theoretical insights into how learning and regularisation can be reframed when we have almost no data to learn from.