Bill Lionheart works on theoretical, numerical and applied aspects on inverse problems in imaging. Current interests include medical imaging, materials science, geophysics,security screening, mine and UXO detection.  The imaging technologies he studies range from low frequency electromagnetics, through microwaves to light and X-rays. Also imaging with particles including neutrons. Recently his interest in “rich tomography” problems have grown. These include many tomographic modalities where for each source and detector pair the measurement is non-scalar; for example a spectrum, diffraction pattern polarization state or time series. This enables non scalar image reconstruction including tensor fields and scattering cross sections.