The several successful solutions to the problem of image reconstruction from projections have caused a rapid growth of a number of new techniques for the reconstruction of distributions and images in several scientific fields. The importance of these techniques, especially in medicine, can hardly be overestimated.
In a new algorithm for image reconstruction from projections [l, 2], a special form of the projection data is employed providing some certain advantages. This new form or map of the projection data are called linograms.
This is intended as an overview of linograms and the algorithm based on them. Thorough discussions of conventional techniques are to be found in [3, 4 and 5]. In conventional techniques for image reconstruction, a two dimensional distribution of some property is reconstructed. The property might be the x-ray attenuation in a cross-section of the body, the distribution of a radioactive substance or something else. The distribution is not directly accessible but it is possible to measure line integrals (rays) through i t. The problem now is to reconstruct the distribution (the image) from i ts line integrals (its projections).
Let the property we are interested in be described by the function f(x, y). projection data are estimates of line integrals of f of known location. Incon~entional techniques each line is specified by two parameters s and e, where s is the (signed) distance from the origin and e its angle with the y-axis.
Linköping: Linköping University Electronic Press , 1988. , 23 p.