Image Reconstruction and Knowledgebase Tomography Mechanism

In this study, the problem of image reconstruction (Inverse Problem) and its semantic relationshipwith a large range of applied and engineering problems are explained. The mechanism of tomographicwhich is an example of the image reconstruction problem is described. The existence and uniqueness ofsolutions and also regularization techniques are discussed. In order to better imagine abstract concepts, the process of digital X-ray imaging is presented using MATLAB. Image reconstruction techniquesare described by Radon and Fourier transforms and algebraic methods. The effects of selecting the number of angles in tomography and additive noise in the data, on the quality of the reconstructed image are investigated. The numerical results and the comparison of images reconstructed by different methods confirm the special ability of algebraic techniques in image reconstruction. In addition, it is shown that in algebraic methods, desirable features such as positivity and smoothness can be considered for the reconstructed image, which has a significant effect on reducing the approximation error.