This field has two distinct research areas, each of which entails multidisciplinary teams in collaboration with hospitals. The first area is mammography. This is used for screening and symptomatic purposes in the detection of breast cancer. Above the age of 47 all women are invited for a 3-yearly screening mammogram, men and women who are symptomatic tend to be referred for a mammogram as it is a primary diagnostic tool. Whilst our research has a particular emphasis on the optimisation of compression force that is applied during the imaging process we also consider related issues too. To date we have discovered several novel facts about the application of compression force. The second area concerns the balancing of X-radiation dose and clinical image quality. X-radiation is used in many aspects of diagnostic imaging however our work only concentrates on specific aspects of computed tomography (CT) and plain radiography. Presently we have a particular interest in low resolution CT for the detection of lung cancer. Our central ambition is to propose ways to produce images for minimal radiation dose whilst preserving diagnostic quality so that they fit for purpose.