Image Processing Toolbox User's Guide |

**Example: Reconstructing an Image from Parallel Projection Data**

The commands below illustrate how to reconstruct an image from parallel projection data. The test image is the Shepp-Logan head phantom, which can be generated by the Image Processing Toolbox function `phantom`

. The phantom image illustrates many of the qualities that are found in real-world tomographic imaging of human heads. The bright elliptical shell along the exterior is analogous to a skull, and the many ellipses inside are analogous to brain features.

- Create a Shepp-Logan head phantom image.
- Compute the Radon transform of the phantom brain for three different sets of theta values.
`R1`

has 18 projections,`R2`

has 36 projections, and`R3`

has 90 projections. theta1 = 0:10:170; [R1,xp] = radon(P,theta1); theta2 = 0:5:175; [R2,xp] = radon(P,theta2); theta3 = 0:2:178; [R3,xp] = radon(P,theta3);

- Display a plot of one of the Radon transforms of the Shepp-Logan head phantom. The following figure shows
`R3`

, the transform with 90 projections.

**Radon Transform of Head Phantom Using 90 Projections
**

- Note how some of the features of the input image appear in this image of the transform. The first column in the Radon transform corresponds to a projection at 0º that is integrating in the vertical direction. The centermost column corresponds to a projection at 90º, which is integrating in the horizontal direction. The projection at 90º has a wider profile than the projection at 0º due to the larger vertical semiaxis of the outermost ellipse of the phantom.

- Reconstruct the head phantom image from the projection data created in step 2 and display the results.

- The following figure shows the results of all three reconstructions. Notice how image
`I1`

, which was reconstructed from only 18 projections, is the least accurate reconstruction. Image`I2`

, which was reconstructed from 36 projections, is better, but it is still not clear enough to discern clearly the small ellipses in the lower portion of the image.`I3`

, reconstructed using 90 projections, most closely resembles the original image. Notice that when the number of projections is relatively small (as in`I1`

and`I2`

), the reconstruction can include some artifacts from the back projection.

**Inverse Radon Transforms of the Shepp-Logan Head Phantom
**

Inverse Radon Transform | Fan-Beam Projection Data |

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