Object motion can cause artifacts in CT images. This happens in part because objec...

Object motion can cause artifacts in CT images. This happens in part because object motion produces an observation that is not a legitimate Radon transform of any object. Assume parallel ray geometry.

(a) Prove that the Radon transform of ? Sketch its sinogram.

(b) Prove the following theorem:

(c) Find the Radon transform of Sketch its sinogram.

We now assume that while the scanner acquires data over θ ∈ [0, π/2]

the object is δ(x, y) and while the scanner acquired data over θ ∈ [π/2, π)

the object is δ(x − 1, y). In other words, the object moved during the scan

from (0, 0) to (1, 0).

(d) Sketch the sinogram that is acquired by this scan.

(e) Prove the following:

(f) Show that the sinogram acquired by the scanner when the object moved cannot be the Radon transform of any object.