Download - Flow Chart of FBP
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Flow Chart of FBP.
![Page 2: Flow Chart of FBP](https://reader036.vdocuments.us/reader036/viewer/2022082320/568139be550346895da163e3/html5/thumbnails/2.jpg)
BME 525 HW 1: Programming assignmentThe Filtered Back-projection Image reconstruction using
Shepp-Logan filter
•You can use any programming languages, Fortran, C , C++ or Matlab ( without employing built-in functions for image reconstruction, radon( ) and iradon( ) ).
Example of steps: Step1 : Creating Phantom image
Hint: - Using an odd sized image might ease computations by
having a center ray. - Make 2 phantom images :
small one for testing program ( 63x63 ) large one for presentation ( 255x255 )
![Page 3: Flow Chart of FBP](https://reader036.vdocuments.us/reader036/viewer/2022082320/568139be550346895da163e3/html5/thumbnails/3.jpg)
Step2 : Calculate Projection data and Construct Sinogram: 1. Define the step-size of angle, theta.2. Define the number of rays per view, m.3. Calculate the projection data
- The projection of the image intensity along a radial line oriented at angle theta k and distance tk from origin. : Line integral
along a line original phantom f(x,y)
- Rotate f(x,y) by a given theta
rotated and interpolated f(x,y)
![Page 4: Flow Chart of FBP](https://reader036.vdocuments.us/reader036/viewer/2022082320/568139be550346895da163e3/html5/thumbnails/4.jpg)
- Sum all pixel values on each row of the rotated and interpolated f(x,y): This is to calculate projection data or ray sums or line integrals.
ray sum
![Page 5: Flow Chart of FBP](https://reader036.vdocuments.us/reader036/viewer/2022082320/568139be550346895da163e3/html5/thumbnails/5.jpg)
4. Construct Sinogram - Sinogram is a collection of Projection data for all theta ( n x m matrix ) - Repeat step 3 for all theta you define
sinogram
![Page 6: Flow Chart of FBP](https://reader036.vdocuments.us/reader036/viewer/2022082320/568139be550346895da163e3/html5/thumbnails/6.jpg)
Step 3: Shepp-Logan filtering and Reconstruct phantom image
1. Design Shepp-Logan fileter HSL(w)
2. Filtering Signogram in frequency or spatial domain.
sinogram before filtering
sinogram after S-L filtering
![Page 7: Flow Chart of FBP](https://reader036.vdocuments.us/reader036/viewer/2022082320/568139be550346895da163e3/html5/thumbnails/7.jpg)
3. Reconstruct image from filtered sinogram.
64*64 256*256Original