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Tomografia geometrica e discreta e applicazioni

**Team**
Paolo Dulio
**Collaboratori esterni**
Paolo Finotelli (Polimi)
Carla Peri (Unicatt)
Silvia M.C. Pagani (Unicatt)

Image reconstruction from projections is one of the main inverse problems which appears in several applications. The image is usually represented by an unknown real valued function $f(x,y)$, with bounded support. The values of $f$ are related to physical properties of a two-dimensional section of the object under investigation. Projections are taken with the help of some kind of rays. For instance, in Computerized Tomography (CT), a portion of a human body is reconstructed by measuring the coefficient of linear attenuation of each beam of the $X$-ray traveling along a line crossing the body. The radiation is produced by photons, issued from a source and collected by a detector, both translating and rotating around the body. The differences between issued and collected photons measure the absorption of radiation by different tissues.

For our purposes, the usual density functions appearing in CT are replaced by geometric objects, and one of the main goal is to find conditions which guarantee a faithful reconstruction, possibly unique, within a given geometric class of geometric subsets.