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26 June 1992 Reconstruction from limited projection data
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Abstract
An outstanding problem in reconstruction methodology is the treatment of incomplete data sets. The inexact reconstruction technique (IRT) allows a stochastic approach, carried out in real space, which provides substantial improvement in reconstruction accuracy when compared to the standard filtered backprojection algorithm. This technique relies specifically on an iterative approach to the treatment of the probability related matrix which is assumed to be proportional to the original density distribution (original object matrix). This is obtained by the summation or multiplication of the set of probability matrices generated by back-projecting the known projections after the usual reorientation to correct for the angular projection to which each corresponds. Employing a Boolean constraint, the largest value in the probability matrix is located and an `l' is placed at the same coordinates in a blank array. This point in the probability matrix is then set to zero and the matrix projections are taken at the same angular orientations followed by re-backprojection to generate a new probability matrix. This process is repeated until the probability matrix is depleted or a specified mass is reached in the reconstructed object. The algorithm requires a considerable amount of computer time due to the necessity of recreating the probability matrix after each point is taken. A compromise solution is to address a certain fraction of the probability matrix to reduce the number of iterations. It has been demonstrated that reasonable results can be obtained when the probability matrix is addressed in increments of 5% or less. In this paper we demonstrate the use of an IRT on the reconstruction of multiple grey level images using limited data sets of from four to sixteen projections.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Oscar H. Kapp and Chin-Tu Chen "Reconstruction from limited projection data", Proc. SPIE 1660, Biomedical Image Processing and Three-Dimensional Microscopy, (26 June 1992); https://doi.org/10.1117/12.59533
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