Figure 16.
Top row: the FBP image from simulation data generated with the continuous Shepp–Logan phantom for 128 views over 180° and a 256-bin detector. A random constant is added to each view following a Gaussian distribution with standard deviation of 10% of the maximum projection value. Bottom row: images reconstructed from the same data set except that the projections are generated from the discrete Shepp–Logan phantom by optimization using the standard ℓ2 data-norm (left) and an ℓ2 norm on the data derivative (right). These 128 × 128 images solve, respectively, equations (11) and (17) where γ = 0.01. Note that the FBP image is unaffected by the view-random, constant background, that the image reconstructed using equation (11) contains significant artifacts and that the image reconstructed using equation (17) also shows fewer artifacts.