PhD Studentship: Customisable and Infinite-dimensional Adversarial AI for Inverse Problems

In practice, many important signals (for example, medical and scientific images) are not observed directly. Instead, one must reconstruct the signal from corrupted and incomplete measurements, in what is called an inverse problem. As there are an infinite number of possible signals which fit the measurements, this can only be made possible by incorporating prior knowledge about the true signal. In this deep learning era, the state-of-the-art is to learn this from data of ground truth signals. One powerful technique for this is adversarial regularisation, which learns how to distinguish realistic signals from unrealistic ones.

In this project, the goal will be to extend the method of adversarial regularisation in two ways, particularly for inverse problems in imaging. The first will be to develop a prompt-able adversarial regulariser, to allow an end user to customise their prior to include knowledge about the signal expressible via, e.g., text. The second will be to extend the adversarial regulariser to infinite-dimensional inverse problems, using the framework of neural operators (which would allow, for example, resolution-invariant adversarial image reconstruction). These extensions raise both practical and theoretical challenges, with much scope to explore many different questions.

Funding notes:

Funding is available through the School of Mathematics for a suitably strong candidate.

The scholarship will cover tuition fees, training support, and a stipend at standard rates for 3-3.5 years;

Candidates are encouraged to make an informal inquiry with Dr Jeremy Budd (j.m.budd@bham.ac.uk).

For application details, please click the above “Apply” button 

References:

Lunz, Sebastian, Ozan Öktem, and Carola-Bibiane Schönlieb. "Adversarial regularizers in inverse problems." Advances in neural information processing systems 31 (2018).

Kim, Jeongsol, et al. "Regularization by texts for latent diffusion inverse solvers." arXiv preprint arXiv:2311.15658 (2023).

Kovachki, Nikola, et al. "Neural operator: Learning maps between function spaces with applications to pdes." Journal of Machine Learning Research 24.89 (2023): 1-97.

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