Method of paired transforms for reconstruction of images from projections: discrete model

An effective method of discrete image reconstruction from its projections is introduced. The method is based on the vector and paired representations of the two-dimensional (2D) image with respect to the 2D discrete Fourier transform. Such representations yield algorithms for image reconstruction by...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on image processing 2003-09, Vol.12 (9), p.985-994
Main Author: Grigoryan, A.M.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Attenuation measurement
Biomedical imaging
Discrete Fourier transforms
Discrete transforms
Exact sciences and technology
Fourier transforms
Image analysis
Image processing
Image reconstruction
Information, signal and communications theory
Iterative methods
Mathematical models
Neural networks
Projection
Signal processing
Telecommunications and information theory
Three dimensional
Tomography
Two dimensional
Two dimensional displays
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An effective method of discrete image reconstruction from its projections is introduced. The method is based on the vector and paired representations of the two-dimensional (2D) image with respect to the 2D discrete Fourier transform. Such representations yield algorithms for image reconstruction by a minimal number of attenuation measurements in certain projections. The proposed algorithms are described in detail for an N/spl times/N image, when N=2/sup r/, r>1. The inverse formulas for image reconstruction are given. The efficiency of the algorithms is expressed in the fact that they require a minimal number of multiplications, or can be implemented without such at all. The problem of discrete image reconstruction is also considered in three-dimensional (3D) space, namely on the 3D torus, where the reconstruction is performed by means of the nonlinear projections that are integral over 3D spirals on the torus.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2003.816017