Flow Chart of
FBP.
BME 525 HW 1: Programming assignment
The 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 )
 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)
- 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
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
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
3. Reconstruct image from filtered sinogram.
Original
64*64
256*256