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

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1 Author(s)
Grigoryan, A.M. ; Dept. of Electr. Eng., Univ. of Texas, San Antonio, TX, USA

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×N image, when N=2r, 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.

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Image Processing, IEEE Transactions on  (Volume:12 ,  Issue: 9 )