X-Ray Computed Tomography

1 / 18

# X-Ray Computed Tomography - PowerPoint PPT Presentation

X-Ray Computed Tomography. Radon Transform Fourier Slice Theorem Backprojection Operator Filtered Backprojection (FBP) Algorithm Implementation Issues Total Variation Reconstruction. X-Ray Tomography. “Tomography” comes from Greek and means cross-sectional representations

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' X-Ray Computed Tomography' - ohio

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

X-Ray Computed Tomography

• Fourier Slice Theorem
• Backprojection Operator
• Filtered Backprojection (FBP) Algorithm
• Implementation Issues
• Total Variation Reconstruction

X-Ray Tomography

• “Tomography” comes from Greek and means cross-sectional representations

of a 3D object

• X-ray tomography, introduced by Hounsfield in 1971, is usually called
• computed tomography (CT)
• CT produces images of human anatonomy with a resolution of about 1mm

and an attenuation coefficient attenuation of about 1%

L

S

body

dl

R

X-Ray Tomography

Fourier Slice Theorem: Consequences

1- The solution of the inverse problem , when exists,

is unique

2- The knowledge of the the Radom transform of implies the

knowledge of the Fourier transform of

is spacelimited

can be computed from samples

taken apart

Fourier Slice Theorem: Consequences

Assumnig that is bandlimited to then it is possible to restore

with a resolution

Backprojection Operator

is the adjoint operator of when the usual inner product is

considered for both the data functions and the objects

Filtered Backprojection Algorithm

periodic function of 

Filtered Backprojection Algorithm

From the Fourier slice theorem

Defining the filtered backprojections as

Then

Filtered Backprojection

Hann filter

Ram-Lak filter