from the origin and its angle of inclination 
, a definition very close to that of the Hough transform
where the delta function defines integration only over the line. The range of is limited to 
. Like in the Hough transform, the Radon operator maps the spatial domain (x,y) to the projection domain ( 
), in which each point corresponds to a straight line in the spatial domain. Conversely, each point in the spatial domain becomes a sine curve in the projection domain, hence the use of the name sinogram.
In tomography, a back-projection operator and the inverse of the Radon transform are used to reconstruct images in three dimensions from intensities recorded in one or two dimensions (see [Barrett81], [Phelps86], [Jain89]).