Discrete 2-D Fourier Transform Separable 2-D transforms Vector forms of representation Partitioning of 2-D transforms Tensor representation of the 2-D DFT Discrete Fourier transform and its geometry Problems Direction Images 2-D direction images on the lattice The inverse tensor transform: Case N is prime 3-D paired representation Complete system of 2-D paired functions Paired transform direction images L-paired representation of the image Problems Image Sampling Along Directions Image reconstruction: Model I Inverse paired transform Example: Image 4 Ã-- 4 Property of the directed multiresolution Example: Image 8 Ã-- 8 Summary of results Equations in the coordinate system (X, 1 − Y ) Problems Main Program of Image Reconstruction The main diagram of the reconstruction Part 1: Image model The coordinate system and rays Part 2: Projection data Part 3: Transformation of geometry Part 4: Linear transformation of projections Part 5: Calculation the 2-D paired transform Fast projection integrals by squares Selection of projections Problems Reconstruction for Prime Size Image Image reconstruction: Model II Example with image 7 Ã-- 7 General algorithm of image reconstruction Program description and image model System of equations Solutions of convolution equations MATLAB R-based code (N prime) Problems Method of Particles Point-map of projections Method of G-rays Reconstruction by field transform Method of circular convolution Problems Methods of Averaging Projections Filtered backprojection BP and method of splitting-signals Method of summation of line-integrals Models with averaging General case: Probability model Problems Bibliography Appendix A Appendix B Index (X, 1 − Y ) Problems Main Program of Image Reconstruction The main diagram of the reconstruction Part 1: Image model The coordinate system and rays Part 2: Projection data Part 3: Transformation of geometry Part 4: Linear transformation of projections Part 5: Calculation the 2-D paired transform Fast projection integrals by squares Selection of projections Problems Reconstruction for Prime Size Image Image reconstruction: Model II Example with image 7 Ã-- 7 General algorithm of image reconstruction Program description and image model System of equations Solutions of convolution equations MATLAB R-based code (N prime) Problems Method of Particles Point-map of projections Method of G-rays Reconstruction by field transform Method of circular convolution Problems Methods of Averaging Projections Filtered backprojection BP and method of splitting-signals Method of summation of line-integrals Models with averaging General case: Probability model Problems Bibliography Appendix A Appendix B Index-map of projections Method of G-rays Reconstruction by field transform Method of circular convolution Problems Methods of Averaging Projections Filtered backprojection BP and method of splitting-signals Method of summation of line-integrals Models with averaging General case: Probability model Problems Bibliography Appendix A Appendix B Index.