Generative Models Applied to Inverse Problems

My research works at the intersection of deep learning and inverse problems in imaging. Solving an inverse problem is the task of computing an unknown physical quantity given indirect measurements via a (usually) known forward model. A typical example is when imaging technologies are used in medicine, engineering, astronomy and geophysics. Interesting Inverse Problems are nearly always ill-posed and addressing this is critical in applications where decision making is based on the recovered image. In particular, sometimes the data recovered is not sufficient to solve the reconstruction problem accurately and some form of prior knowledge about the object must be incorporated in the solution process. Developing new and improving existing approaches to these cases is the aim of my project.

The proposed approaches uses deep learning methods to learn a generative model. Generative models implicitly model high-dimensional distributions of data from observations. The learnt distribution can then be used as a prior when solving the inverse problem, ensuring solutions are feasible. Learnt priors could provide more specific information than that of a hand-crafted prior while remaining flexible to changes in the forward problem. For example, we could learn a generative model that can produce all feasible brain heart and lung CT images. Then receiving low radiation dose data from the CT scanner, we search through the set of feasible images to find the image that best fits the data. The resulting image will be high quality despite the small amount of provided data.

There is wide scope for novel engineering and/or physical sciences research. The resulting optimisation required for finding the image produced by the generative model that best fits the data is both a non-linear and non-convex problem and will require application or development of state of the art techniques. Numerical analysis tools are needed to bound errors and convergence. Mathematical approaches working closely with computer scientists also need to be developed for checking and ensuring that the ground truth images can be produced by the generative model. This will add to a fast growing research area including variational autoencoders and generative adversarial networks.

The impact of the SAMBa CDT will occur principally through the following two pathways:

1. Direct engagement with industrial partners, leading to PhD projects that are collaborative with industry, and that are focussed on topics with direct industrial impact.

2. The production of PhD graduates with
(a) the mathematical, statistical and computational technical skill sets that have been identified as in crucial demand both by EPSRC and by our industrial partners, coupled to
(b) extensive experience of industrial collaboration.

The underlying opportunity that SAMBa provides is to train graduates to have the ability to combine complex models with 'big data'. Such people will be uniquely equipped to deliver impact: whether they continue with academic careers or move directly to posts in industry, through quantitative modelling, they will provide the information that gives UK businesses competitive advantages. Our industrial partners make it clear to us that competitiveness in the energy, manufacturing, service, retail and financial sectors is increasingly dependent on who can best and most quickly analyse the huge datasets made available by the present information revolution.

During their training as part of SAMBa, these students will have already gained experience of industrial collaboration, through their PhD projects and/or the Integrated Think Tanks (ITTs) that we propose, that will give all SAMBa students opportunities to develop these transferable skills. PhD projects that involve industrial collaboration, whether arising from ITTs or not, will themselves deliver economic and social benefits to UK through the private companies and public sector organisations with which SAMBa will collaborate.

We emphasise that Bath is at the forefront of knowledge transfer (KT) activities of the kind needed to translate our research into impact. Our KT agenda has recently been supported by KT Accounts and Impact Acceleration Accounts from EPSRC (£4.9M in total) and a current HEFCE HEIF allocation of £2.4M. Bath is at the forefront of UK activity in KTPs, having completed 150 and currently holding 16 KTP contracts worth around £2.5M.

The SAMBa ITTs are an exciting new mechanism through which we will actively look for opportunities to turn industrial links into research partnerships, supported in the design of these projects by the substantial experience available across the University.

More widely, we envisage impact stemming from a range of other activities within SAMBa:

- We will look to feed the results of projects involving ecological or epidemiological data directly into environmental and public health policy. We have done this successfully many times and have three REF Case Studies describing work of this nature.

- Students will be encouraged to make statistical tools available as open source software. This will promote dissemination of their research results, particularly beyond academia. There is plenty of recent evidence that such packages are taken up and used.

- Students will discuss how to use new media to promote the public understanding of science, for example contributing to projects such as Wikipedia.

- Students will be encouraged to engage in at least one outreach activity. Bath is well known for its varied, and EPSRC-supported, public engagement activities that include Royal Institution Masterclasses, coaching the UK Mathematics Olympiad team, and reaching 50 000 people in ten days with an exhibit at the Royal Society's 350th Anniversary Summer Exhibition in 2010.