A new Radon transform result

A convex elliptical region of the plane supports a positive-valued function of two variables whose Radon transform depends only on the slope of the integrating line: any two parallel lines that intersect the ellipse generate equal line integrals of the function. It is somewhat surprising that such a function exists. It is even more surprising, as we show in this paper, that the elliptical region is the only convex compact planar set that supports such a function. We discovered this result while attempting to extend an analytical solution technique for a 2-D integral equation that figures in a certain problem of motion detection in a noisy image sequence