Linograms in image reconstruction from projections. 1. Back projecting using the Radon transform

The notion of linogram is introduced. It corresponds to the notion of a sinogram in the conventional representation of projection data in image reconstruction. In the sinogram the points corresponding to rays that go through a fixed point in the cross section to be reconstructed all fall on a sinusoidal curve. In the linogram, however, these points fall on a straight line, so back projection corresponds to integration along straight lines in the linogram. A theorem is described which expresses the back projection operator in terms of the Radon transform and simple changes of variables. A novel image reconstruction method based on the theorem is introduced