Computed tomography refers to the imaging of slices of an object by exposing them to X-ray in different directions. Measurement of image quality is one of great importance in the field of medical applications. In applications such as CT and MRI scanning, most of the time the quality of reconstructed image is assessed qualitatively by radiologist or domain experts which are purely subjective evaluation. The FBP algorithm produces excellent quality and high performance reconstruction compared with other reconstruction algorithms. This thesis presents different projection types (fan beam geometry, and cone beam geometry) for the image reconstruction, the geometries are calculated analytically by specified 2D head phantom for fan beam and 3D head phantom for single slice spiral cone beam geometry with different ranges covering angle. In the thesis the FBP algorithm was applied with the fan beam and single slice geometries. Different types of filters (Hann, Hamming, Kaiser, Cosine, Ram-Lak, and Gaussian) are used in the algorithm and a new window filter is proposed in the algorithm. Comparisons are made between the new window and different common windows by quality measurement to get a reconstructed image with high quality and high performance suitable for the implementation of the FBP. A computer programs has been designed, written, and implemented in this work using MATLAB 7.1, for fan beam and single slice projections. Good results of quality and performance were obtained for the tomographic reconstructed image from its projection on CT scanner.