UE Medical imaging: tomography and 3D reconstruction from 2D projections

Degrees incorporating this pedagocial element :


CT Scanners and nuclear imaging (SPECT and PET) have greatly improved medical diagnoses and surgical planning. Mathematics is necessary for these medical imaging systems to deliver images. We present mathematical problems arising from these medical imaging systems. We show how to reconstruct images from projections of the attenuation function in radiology or respectively of the activity in nuclear imaging. We present recent advances in 2D and 3D reconstruction problems.

Evaluation :

2 hours written exam (E) and a preliminary test (P). The final mark in session 1 is obtained by max(.75*E1+.25*P,E1). The final mark in session 2 is obtained by E2, a session 2 written exam only.


Basic knowledge in analysis, integration, Fourier analysis, elementary 2D an 3D geometry is required.

Targeted skills

At the end of the course, the student will have acquired knowledge about CT scanners and Cone Beam CT reconstruction in medical imaging. They will be able to perform 2D and 3D reconstructions of a function from sets of its projections, including modern Region of Interest problems. They will know the range conditions of some projection operators. They will be able to apply the range conditions for the identification of some parameters of the projection model.


C. Epstein, Introduction to the mathematics of medical imaging, SIAM

F. Natterer The mathematics of Computerized Tomography, SIAM