Limited Angle Reconstruction Sample Clauses

Limited Angle Reconstruction. ‌ In addition to the full CT case, it is important to also consider the case of limited angle reconstructions. Specifically, in the area of digital tomography, the limited angle reconstruction known as tomosynthesis has become an important diagnostic tool in breast imaging. The motivations for limited angle reconstruction are to reduce radiation dose to patients as well as to reduce the cost of this procedure. The limited angle reconstruction provides significantly more challenges to image reconstruction because the mathematical problems is much more ill-posed than the full CT case. This also means that the reconstruction quality is much more sensitive to the noise. In addition, the original objective function might have more stationary points and several of them are likely to satisfy the KKT condition. Under this situation, when the problem is effectively underdetermined, a poor initial guess may lead to an undesirable local minimum. To test the limited angle reconstruction, the same test problem is used but with fewer projection angles. We shrink the projection angles from 180 degrees to 90 degrees, which ranges from 0 to 90 degrees. Furthermore, Poisson distribution is used to generate the projection data. After implementing the previous algorithm, the reconstructed images are presented in Figure 3.7. 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.1 Figure 3.7: The reconstructed images for air (upper left), adipose (upper right) and calcium (middle) with 90 degrees projection. From Figure 3.7, we can clearly see that the reconstructed images obtained from the limited angle case are more blurred than the images from the full CT case. As expected, with fewer projection angles, the images are of poorer quality. For the 90 degrees case, we can basically identify the distributions of materials roughly, while the details are more difficult to recognize. Only the material map of calcium is nearly fully separated from other materials. Moreover, we can see that the boundaries of different materials are not as clear as the boundaries in the full CT case. In several areas, the pixels are surrounded by shadows, which means that the materials are not completely separated. In the area of mixture, several pixels are colorful and the results depart slightly from the true solution. However, it is well known that due to the limited angle data, there are fundamental limitations when computing reconstructions [20]. Air Adipose Calcium