Computed Tomography

I compare transmission, emission, and magnetic resonance tomography from the viewpoint of a mathematician. The choice of model is crucial; there is for any 0 = the inverse of the function (x,y) = 1 with compact support in the plane, a g(x,y) = 0 or 1 only, with support contained in that of the inverse of the function, and with the same line integrals as the inverse of the function in any of n given directions. Yet there is only one function g(x,y) with 0 = g = 1 with the same horizontal and vertical projections as that of the indicator of the unit disk. Some Soviet work has been useful.