Image Processing: Tensor Transform And Discrete Tomography With Matlab ®
by Artyom M. Grigoryan /
2012 / English / PDF
4.6 MB Download
Focusing on mathematical methods in computer tomography,
Focusing on mathematical methods in computer tomography,Image Processing: Tensor Transform and Discrete
Tomography with MATLAB
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.
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
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.
-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.
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.
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.