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Viser: Image Processing - Tensor Transform and Discrete Tomography with MATLAB ®
Image Processing
Tensor Transform and Discrete Tomography with MATLAB ®
Artyom M. Grigoryan og Merughan M. Grigoryan
(2018)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- Paperback: 466 sider
- Udgiver: CRC Press LLC (April 2018)
- Forfattere: Artyom M. Grigoryan og Merughan M. Grigoryan
- ISBN: 9781138076174
Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB® introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more quickly and accurately reconstruct images from a finite number of projections, thereby avoiding overradiation of the body during a computed tomography (CT) scan.
The book presents several new ideas, concepts, and methods, many of which have not been published elsewhere. New concepts include methods of transferring the geometry of rays from the plane to the Cartesian lattice, the point map of projections, the particle and its field function, and the statistical model of averaging. The authors supply numerous examples, MATLAB®-based programs, end-of-chapter problems, and experimental results of implementation.
The main approach for image reconstruction proposed by the authors differs from existing methods of back-projection, iterative reconstruction, and Fourier and Radon filtering. In this book, the authors explain how to process each projection by a system of linear equations, or linear convolutions, to calculate the corresponding part of the 2-D tensor or paired transform of the discrete image. They then describe how to calculate the inverse transform to obtain the reconstruction. The proposed models for image reconstruction from projections are simple and result in more accurate reconstructions.
Introducing a new theory and methods of image reconstruction, this book provides a solid grounding for those interested in further research and in obtaining new results. It encourages readers to develop effective applications of these methods in CT.
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