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Focusing on mathematical methods in computer tomography, this book introduces novel approaches to help solve the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more accurately reconstruct images from a finite number of projections and avoid overradiating the body during a CT scan. The book presents several new concepts and methods, including 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.
Artyom M. Grigoryan, Ph.D., is currently an associate professor at the Department of Electrical Engineering, University of Texas at San Antonio. He has authored or co-authored three books, including Brief Notes in Advanced DSP: Fourier Analysis with MATLAB® (2009) and Multidimensional Discrete Unitary Transforms: Representation: Partitioning, and Algorithms (2003) as well as two book chapters and many journal papers. He specializes in the theory and application of fast one- and multi-dimensional Fourier transforms, elliptic Fourier transforms, tensor and paired transforms, integer unitary heap transforms, design of robust linear and nonlinear filters, image encryption, computerized 2-D and 3-D tomography, and processing of biomedical images. Merughan M. Grigoryan is currently conducting research on the theory and application of quantum mechanics in signal processing, differential equations, Fourier analysis, elliptic Fourier transforms, Hadamard matrices, fast integer unitary transformations, the theory and methods of the fast unitary transforms generated by signals, and methods of encoding in cryptography. He is the coauthor of the book Brief Notes in Advanced DSP: Fourier Analysis with MATLAB® (2009).
Discrete 2-D Fourier Transform. Direction Images. Image Sampling Along Directions. Main Program of Image Reconstruction. Reconstruction for Prime Size Image. Method of Particles. Methods of Averaging Projections. Bibliography. Appendices. Index.
