1. Flow Chart of FBP.

2. 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 )

3.  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 t k 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)

4. - 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

5. 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

6.  Step 3: Shepp-Logan filtering and Reconstruct phantom image 1. Design Shepp-Logan fileter H SL (w) 2. Filtering Signogram in frequency or spatial domain. sinogram before filtering sinogram after S-L filtering

7. 3. Reconstruct image from filtered sinogram. 64*64256*256 Original