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Strategies for Tomography

Image reconstruction from collected data is an inverse problem that frequently appears in several applications. It is encountered in various research areas, such as biomedical imaging, reconstruction algorithms, image processing, stereology, and mathematical morphology. It turns out that the same methodologies and strategies can be frequently adapted to different frames and disciplines. One of the main tools is the Radon Transform, and its inversion formula which is used, in particular, in many problems of tomographic research where the information is usually acquired by means of data obtained from X-rays projections. Since the 1990s specialistic meetings have been organized devoted to both theoretical advances and practical applications of Tomography. Among them, the Meeting on Tomography and Applications, now in its 6th edition, succeeds in attracting some of the main researchers involved in the various aspects of Tomography. The presentations consists of technical contributions as well as talks outlining the state-ofthe-arts and proposing future research directions. The main purpose of this edition of the meeting was to focus on connections and overlaps among Discrete Tomography, Geometric Tomography, and Computerized Tomography, with a special focus on applications. This special issue consists of invited papers. Some of them have been presented at the 6th Meeting on Tomography and Applications held at Politecnico di Milano on April 26-27, 2012, but in order to provide a better perspective on current research also additional papers were invited. The papers went through a thorough refereeing process and the accepted papers are presented in this issue. The reminder of this preface consists of two parts. In the first part we provide brief overviews for each of the papers from this issue. In the second part we provide summaries for talks presented at the 6th Meeting on Tomography and Applications. In this way the reader can get a better insight into the nature of the meeting and hence also into the current research in the area covered by this special issue.