Algorithms for image reconstruction.

Three-dimensional (3D) imaging is becoming one of the most important applications of radioactive materials in medicine. It offers good spatial resolution, a 3D insight into the human body, and a high sensitivity in the picomolar range because markers for biological processes can be detected well when labeled with radioactive materials. In addition, the technical equipment has undergone many technological achievements. This is true for single-photon emission computed tomography (SPECT), positron emission tomography (PET), and X-ray computed tomography (CT), which is often used in connection with the nuclear medical imaging systems, as also described in chapter 5 about sources in nuclear medicine. As can be realized by the names of the systems, the imaging methodologies all generate the images using a computational process. This is necessary since in all types of CT the purpose is to generate a stack of two-dimensional slices (a 3D data set) that are reconstructed from various 'projections' along certain lines. This reconstruction process can be achieved by various different methods, which can be divided into so-called algebraic or iterative reconstruction methods and analytical methods. After a brief introduction to give an approach to the reconstruction task in general, we describe both kinds of algorithms