The aim of classical tomography is to recover the inner structure of a physical body from X-ray images taken from all around the body. The mathematical model behind tomography, applicable to a wide range of practical applications, is to reconstruct a function from the knowledge of integrals of the function over a collection of lines. This is an ill-posed inverse problem, especially so if the collection of lines is restricted. Such restrictions arise for example in medical imaging when the radiation dose to the patient is minimized. In recent years, many powerful regularization methods have been proposed for tomographic reconstruction. Discussed here are total (generalized) variation regularization and sparsity-promoting methods using multiscale transforms such as wavelets and shearlets. A low-dose 3D dental X-ray imaging product is presented as a practical example.
Joint ACA-cmih seminar