| 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. |
| About the speaker |
Angelica Aviles-Rivero is an Assistant Professor at the Yau Mathematical Sciences Center,
Tsinghua University. Previously, she was a Senior Research Associate at the Department of
Applied Mathematics and Theoretical Physics, University of Cambridge. She is a member of
ELLIS. Her research lies at the intersection of applied mathematics and machine learning,
focusing on developing data-driven algorithmic techniques that enable computers to extract highlevel
understanding from vast datasets. Her research has been highlighted, including receiving
an Outstanding Paper Award at ICML 2020. She was elected as an officer for the SIAM SIAG/IS
secretary position for the term 2023. For more information visit:
https://angelicaiaviles.wordpress.com/
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