Image Processing: Tensor Transform and Discrete Tomography with MATLAB ®

Artyom M. Grigoryan, Merughan M. Grigoryan

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October 15, 2012 by CRC Press
Reference - 466 Pages - 233 B/W Illustrations
ISBN 9781466509948 - CAT# K14749

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Features

  • Introduces new concepts and novel approaches for solving the problem of image reconstruction on the Cartesian lattice
  • Describes new algorithms and MATLAB®-based codes that can be effectively used in practice
  • Presents the idea of transferring the geometry of rays in the general case of rays with non-zero width
  • Discusses the challenges of implementing the proposed ideas for the fan beam projection scheme and 3-D image reconstruction
  • Includes study problems for computer simulation
  • Proposes new directions for research in the field of computed tomography
  • Contains more than 230 black-and-white illustrations and an eight-page color insert

Summary

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.