Professor Bill Lionheart
Bill Lionheart (William R.B. Lionheart, FIAM, FIET) is a professor of applied mathematics at Manchester specializing in inverse problems in imaging.
When asked what he does he usually says “make 3D images of inside something from measuring outside”. X-ray tomography is a typical example which translates in to the mathematical problem of finding a function of three variables from averages along lines. He is interested in a wide range of applications, scales and different physical measurements. He helped develop a fast 3D baggage scanner now deployed widely in airports around the world, he has worked for many decades on electrical imaging in medicine now used for lung monitoring in intensive care. With colleagues he has developed new civilian land mine detectors with a field prototype and a lot of mathematics. He is currently working on proton therapy dose imaging, 3D radar imaging and many problems in rich tomography were one seeks to find much more than a scalar image, such as stress tensor or texture in a crystalline solid. His work spans analysis, geometry, numerics as well as practical applications. He is delighted when he also has to use abstract algebra!
His work is supported by grants including Rich nonlinear tomography for advanced materials (awarded by EPSRC) and Next generation imaging for real-time dose verification enabling adaptive proton therapy (UKRI EU Horizon Europe Guarantee award).
Select publications
- Wensrich, Christopher and Holman, Sean and Lionheart, William and Luzin, Vladimir and Cuskelly, Dylan and Kirstein, Oliver and Salvemini, Filomena, Well-Posedness and Trivial Solutions to Inverse Eigenstrain Problems. International Journal of Solids and Structures, in press, http://dx.doi.org/10.2139/ssrn.5182545
- Setterdahl, L. M., Lionheart, W. R., Lathouwers, D., Ratliff, H. N., Skjerdal, K., & Meric, I. (2025). Evaluating impact of detector arrangement and position resolution effect on a fast neutron-based range verification system for proton therapy. Radiation Physics and Chemistry, 234, 112793.
- Watson, F. M., Daniel Andre, and William Robert Breckon Lionheart. “Resolving full-wave through-wall transmission effects in multi-static synthetic aperture radar.” Inverse Problems 40.8 (2024): 085009.
- Wensrich, C. M., Holman, S., Courdurier, M., Lionheart, W. R., Polyakova, A. P., & Svetov, I. E. (2024). Direct inversion of the Longitudinal Ray Transform for 2D residual elastic strain fields. Inverse Problems, 40(7), 075011.
- Watson, F. M., J. Hellier, and W. R. B. Lionheart. “On regularisation of coherent imagery with proximal methods.” Inverse Problems 41.6 (2025): 065005.
- Ledger, Paul David, and William RB Lionheart. “Characterising small objects in the regime between the eddy current model and wave propagation.” European Journal of Applied Mathematics 35.2 (2024): 294-317.
- Özdeğer, T., Davidson, J. L., Ledger, P. D., Conniffe, D., Lionheart, W. R., & Peyton, A. J. (2023). Measuring the magnetic polarizability tensor of nonsymmetrical metallic objects. IEEE Sensors Journal, 23(17), 20027-20036.
- Turko, J. A. B., Meric, I., Alagoz, E., Hysing, L., Lathouwers, D., Lionheart, W., … & Kögler, T. J. (2023, November). The NOVO project-hybrid neutron/gamma-ray imaging for range verification in particle therapy. In 2023 IEEE Nuclear Science Symposium, Medical Imaging Conference and International Symposium on Room-Temperature Semiconductor Detectors (NSS MIC RTSD) (pp. 1-2). IEEE.
