Lecture 12: Central Section Theorem

Question 1

When is there enough information in a projection to construct an image in real space?

Answer 1

When k-space is filled.

Question 2

How is k-space filled by an x-ray CT scanner?

Answer 2

Projections are taken at a sufficient number of angles through the object to fill k-space after being Fourier transformed.

Question 3

Define crude back projection

Answer 3

The generation of a crude image of an object by summing the result of spreading each projection back across the image space.

Question 4

Define filtered back projection

Answer 4

Back projection where an alternate projection, P’, is used rather than P. This projection is filtered where the components are amplified in proportion to their spatial frequency.

Question 5

Describe the shape of the filter used in filtered back projection

Answer 5