Finally, using the definition of the 2D Fourier transform yields

$equation$

In the polar coordinate system, the central slice theorem can be expressed as

$equation$

### 2.6.4Derivation of the FBP algorithm

$equation$

Because $equation$ we have

$equation$

By using the central slice theorem, we can replace F by P:

$equation$

We recognize that ω| is the ramp filter. Let Q(ω, θ)=|ω|P(ω

Get Image Reconstruction now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.