Reconstruction of smooth distributions from a limited number of projections
Applied Optics, Vol. 27, Issue 19, pp. 4084-4097 (1988)
http://dx.doi.org/10.1364/AO.27.004084
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Abstract
Two reconstruction methods that recognize smoothness to be a priori information and use numerically space-limited basis functions have been developed. The first method is a modification of the well-known convolution method and uses such basis functions for the projections. The second method is a continuous algebraic reconstruction technique that employs consistent basis functions for the projections as well as the distribution and makes use of other a priori information like the constraints on the domain as well as the range of the distribution in a rigorous way. The efficacy of these methods has been demonstrated using a limited number of projections synthetically generated from a distribution phantom.
© 1988 Optical Society of America
History
Original Manuscript: November 16, 1987
Published: October 1, 1988
Citation
M. Ravichandran and F. C. Gouldin, "Reconstruction of smooth distributions from a limited number of projections," Appl. Opt. 27, 4084-4097 (1988)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-27-19-4084
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References
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- It should be noted that the modified inversion formula is not equivalent to the standard CBP inversion formula [Eq. (7)] with W(R) in Eq. (8) replaced by the Kaiser window.
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- In the context of ARTs, Censor (1983) characterizes typical projection matrices to be ~105 × 105 with <1% nonzero elements. In our test problems, C is ~102 × 102 with ~30% nonzero elements.
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- For example, some of the 2-D basis function coefficients representing certain regions of the domain of the distribution may be known to be more important than the others.
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- For example, S. No. 4 of Table I with a D matrix size of 102 × 97 and ninety-seven non-negativity constraints required ≈30s for this step on an IBM 4341 machine.
- The quantity 1/σi has been factored out from the coefficients as well as their standard deviations.
- The projection data are free of external errors, but the use of numerically space-limited basis functions introduces internal errors whose standard deviation is estimated to be ≈1.5 × 10−4.
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