Tomography. Larry Shepp Prof of Statistics Rutgers University. Tomography. The Radon transform is the key technology in CAT scanning, now used in every hospital since 1972. Nowadays the research frontier has shifted to MRI= magnetic resonance imaging. I will discuss both.
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Prof of Statistics
Hounsfield invented tomography but didn’t think of using an anatomical model. This idea turned out useful. The line integrals can be calculated exactly. Errors in algorithm can be separated from errors due to noise in data.
Seems pretty silly, but I got very lucky with this idea as we’ll see.
is equal to the two-dimensional Fourier transform of the object.
Thus we know the Fourier transform of f. Now the Fourier inversion formula gives f
In polar coordinates
the product of f ^ with
f(x,y) = sum over L of c(L,(x,y) ) Pf(L), and we need only to know the coefficients c(L,x,y) of the inverse. These depend only on the distance from (x,y) to L. The filter function is the function of the distance.