The Radon transform has encountered many trials to change its ill-posed nature into a well-posed problem. Recovering an initial bulk of data (medical, astronomy, seismology, quality control, etc.) from a set of projections has been an important vector of progress during the last fifty years. However, for a specific implementation the tomographist has to study three different kinds of problems. The first one is the geometry of acquisition (dimension of the initial data, number and angles of projections, spatial position of the bins) and the way to represent it in an adequate manner on the computer. This leads to the expression of a specific discrete Radon operator which (generally) has lost its properties of linearity and shift-invariance; at most, it would tends to the continuous operator if you had an infinite number of projections, pixels, bins. Second, the acquisition device has to be modeled and all kind of new non-linearities have to be taken into account (blur of the detector, attenuation process, mismatch of the projection of the center of rotation, etc.). Third, noise appears. Then things are going from bad to worse. Effectively, if the first step has not been made correctly, the discrepancy between the continuous and discrete (implemented) inverse Radon transform will be responsible for a significant amount of errors into the pixel reconstructed value. Even if this error is low (say 5%), since the radiations that you are giving to a patient (respectively receiving from stars) are low, the contrast sensibility on the image where the medical doctor (resp. the astronomer) want to perform a given task of tumor (resp. double stars) detection of is low. Thus, the first step in this overall process is to perform the computer imagery as better than you can since it is the parameter that you have in hands.