Analytical Image Reconstruction Methods 41 Simple Backprojection Method

The simple backprojection method simply takes each of the measured projection data values and spreads it uniformly over the image pixels that lie along the projection ray passing through the projection bin. This is the method used by Kuhl and Edwards in reconstructing the first brain SPECT data acquired using the MARK IV system.7 To understand why the reconstructed images were less than desirable, we can write the simple backprojection image in polar coordinates as fn(r,f) = Bpj{pe(s)}

where Bpj is the backprojection operation and Pu(vr) is the 1D FT of pu(r) and we have used the fact that t = x cos U + y sin U.

Since the 2D inverse FT, FT^, of Pu(vr) in polar coordinates is given by p(x,y)

\Vr\P(Vr,9)ejvr(x cos 9+y sin 9)d Vrd9 = FT^fP^rß)} (11)

Equation (10) can be written as fB(x,y)

Using the relationship vx = ns cos U and vy = ns sin U Eqn. (9), we find

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