Strip and line path integrals with a square pixel matrix: a unified theory for computational CT projections.

Calculated forward projection techniques have been used for various purposes in computerized tomography applications, and several models have been proposed to simulate the tomography projection process. Since the area weighted strip integral is one of the best models, methods to facilitate the computation of strip integrals would be very useful. In particular, a triangular subtraction technique with a reduced number of weighting factors is proposed for the calculation of the strip integral. A unified path integral theory is also proposed to bridge various models and to clarify the integral interaction when a line or a strip passes through a square pixel matrix.

[1]  P. Joseph,et al.  A Method for Correcting Bone Induced Artifacts in Computed Tomography Scanners , 1978, Journal of computer assisted tomography.

[2]  A. Lent,et al.  ART: Mathematics and applications a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques , 1973 .

[3]  A. Macovski,et al.  A Method for Stop-Action Imaging of the Heart Using Gated Computed Tomography , 1981, IEEE Transactions on Biomedical Engineering.

[4]  C R Crawford,et al.  Reprojection using a parallel backprojector. , 1986, Medical physics.

[5]  B. F. Logan,et al.  The Fourier reconstruction of a head section , 1974 .

[6]  Y. S. Kwoh,et al.  X-Ray Reconstruction of the Spinal Cord, Using Bone Suppression , 1980, IEEE Transactions on Biomedical Engineering.

[7]  T. M. Peters.  Algorithms for Fast Back- and Re-Projection in Computed Tomography , 1981 .

[8]  R H Huesman,et al.  The effects of a finite number of projection angles and finite lateral sampling of projections on the propagation of statistical errors in transverse section reconstruction. , 1977, Physics in medicine and biology.

[9]  R B Schwinger,et al.  Area weighted convolutional interpolation for data reprojection in single photon emission computed tomography. , 1986, Medical physics.

[10]  F. Harris.  On the use of windows for harmonic analysis with the discrete Fourier transform , 1978, Proceedings of the IEEE.

[11]  Albert Macovski,et al.  Iterative Reconstruction-Reprojection: An Algorithm for Limited Data Cardiac-Computed Tomography , 1982, IEEE Transactions on Biomedical Engineering.

[12]  G. Herman,et al.  Convolution reconstruction techniques for divergent beams. , 1976, Computers in biology and medicine.

[13]  R. Gordon.  A tutorial on art (algebraic reconstruction techniques) , 1974 .

[14]  P M Joseph,et al.  The effects of sampling on CT images. , 1980, Computerized tomography.

[15]  Graeme C. Mc Kinnon,et al.  Towards Imaging the Beating Heart Usefully with a Conventional CT Scanner , 1981, IEEE Transactions on Biomedical Engineering.

[16]  Y. S. Kwoh,et al.  A generalized |ω|-filter for 3-D reconstruction , 1977, IEEE Transactions on Nuclear Science.

[17]  P. Joseph.  An Improved Algorithm for Reprojecting Rays through Pixel Images , 1982 .

[18]  G. N. Ramachandran,et al.  Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms. , 1971, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Azriel Rosenfeld,et al.  Digital Picture Processing , 1976 .