Computer Modelling in Tomography and Ill Posed Problems

The last decades of the 20th century were marked by the appearance of a new field of mathematics: computerized tomography. Its theory forms the basis for the solution of many applied problems. The methods of computerized tomography make it possible study the interior structure of a body by examining the characteristics of radiation passing through the object under study (transmission tomography). Depending on the type of radiation used, X-ray, optical, seismic, and some other kinds of tomography can be distinguished. Comparatively weakly researched, untraditional tomography problems are being solved because of new achievements in calculation mathematics and the theory of ill-posed problems (3D cone-beam tomography, geo-tomography). Experiments show possibilities and applicability of algorithms of processing tomography data. This monograph is devoted to considering these problems in connection with series of ill-posed problems in tomography settings, arising from practice. The basic themes of the book are: mathematical basis of the method of computerized tomography; algorithms for 3D cone-beam tomography; and inverse kinematics problems in tomographic settings (geo-tomography). This volume in the Inverse and Ill-Posed Problems Series will be of interest to researchers, graduates and post-graduates in X-ray, optical, seismic, as well as some other kinds of tomography in both academia and industry.