Computed Tomography has made a revolutionary impact on medical diagnosis and has also been used in industrial non-destructive testing. Algebraic reconstruction algorithms for tomography provide better quality images than  conventional reconstruction methods which are based on Fourier techniques, mainly when the measurement has fewer projections or there are noisy conditions. However, in practice, algebraic reconstruction methods are not as widespread as Fourier based ones because of their high computational cost.

The study developed in this thesis deals with several approaches to the reduction of the computation cost associated with algebraic methods. This reduction is obtained by using an alternative system matrix model. We propose new matrix models aiming at this objective. These models are designed using alternative grids of pixels and pixels shapes different from the Cartesian ones. All grids of pixels which are proposed allow ones to employ all scanner symmetries for the calculation of the system matrix. Thus, the matrix volume, which is necessary for the reconstruction algorithm, is reduced.

The proposed matrix models are compared among themselves by means of the simulated and real data reconstruction. These measurements are calculated and obtained from a high-resolution small animal CT and a CT-simulator. The reconstructed images from simulated signals make it possible to measure the quality of the reconstructed images with regard to contrast, resolution and accuracy. As a result of this comparison, the system matrix model which leads to lowest computational cost without jeopardizing the quality requirements, is presented and extended to the 3D case.

Additionally, the designed grid leads to the proposal of a technique which makes it possible to avoid unnecessary operations. This technique consists in finding the border of the region of interest, which implies to confine the image area as well as the projection area, from an individualized analysis of each measurement.

The result produced by the new system matrix model shows that this schema permits to reduce the computational cost associated with algebraic methods. This reduction does not involve reconstructed images with less quality than those images obtained from the Cartesian matrix. In addition, the technique of delimiting the reconstructed area allows for decreasing the number of operations required in the reconstruction process.