Flow Chart of FBP.

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 )

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.

64*64 256*256Original