<< Chapter < Page Chapter >> Page >

Theory of filtered backprojection algorithm (fbp)

The FBP algorithm allows us to take the projections, PӨ(t), developed in the previous sections andreconstruct the original image, f(x,y).

A key idea is the Fourier Slice Theorem. It says that the Fourier Transform of a projection at an angle thetais equivalent to the values of the 2-dimensional Fourier Transform of the image evaluated along a radial line of the same angle.Knowing this fact, we are able to obtain the Fourier Transform of the image, F(u,v), from projections taken at multipleangles.

We start with 2-dimensional Inverse Fourier Transform:

Since we have projections for given angles, a change to polar coordinates is useful.

Using symmetry, this simplifies to:

Using the Fourier Slice Theorem, we substitute in the Fourier Transform of the projection,SӨ(ω).

With this formula, we are now able to reconstruct the original image. We now see that that the FPBalgorithm has certain benefits. We can begin reconstructing the image after the first projection has been calculated, since theimage is built up by summing over all the angles. This could increase speed and practicality for real time applications.

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Terahertz ray reflection computerized tomography. OpenStax CNX. Dec 12, 2005 Download for free at http://cnx.org/content/col10312/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Terahertz ray reflection computerized tomography' conversation and receive update notifications?

Ask