Flow Chart of FBP BME 525 HW 1

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: Ø Step 1 : 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 ( 63 x 63 ) large one for presentation ( 255 x 255 )

Ø Step 2 : 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

ØStep 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