Tomographic imaging uses X-rays to reveal the internal structure of an object. It is widely used in medicine (CT scans) and industry today. However, almost all tomography devices require that the target does not move during imaging. This is because traditional mathematical methods for tomographic image formation assume data collected of the target from many directions, and changing the imaging direction takes time.
We will develop new mathematical methods that allow movement in the target. Then the measurement information is not sufficient for recovering both the structure and dynamics of the target. The new methods are based on complementing the missing measurement data with other information about the target. For example, we may enforce the reconstructed target to be formed of smoothly varying domains with crisp, gradually changing boundaries between them.
The new methods have applications in medical imaging and nondestructive testing. There is a large commercial potential.