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Flow Chart of FBP.

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( ) ).

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Flow Chart of FBP.

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  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 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)

  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 HSL(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*64 256*256 Original

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