TY - JOUR

T1 - A geometric projection-space reconstruction algorithm

AU - Prince, Jerry L.

AU - Willsky, Alan S.

N1 - Funding Information:
*This research was supported by the National Science Foundation grant ECS-87-00903 and the U.S. Army Research Office grant DAAL03-86-K-1071. In addition, the work of the first author was partially supported by a U.S. Army Research Office Fellowship. ‘Now with the Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, MD 21218.

PY - 1990/3

Y1 - 1990/3

N2 - We present a method to reconstruct images from finite sets of noisy projections that may be available only over limited or sparse angles. The algorithm calculates the maximum a posteriori (MAP) estimate of the full sinogram (which is an image of the 2-D Radon transform of the object) from the available data. It is implemented using a primal-dual constrained optimization procedure that solves a partial differential equation in the primal phase with an efficient local relaxation algorithm and uses a simple Lagrange-multiplier update in the dual phase. The sinogram prior probability is given by a Markov random field (MRF) that includes information about the mass, center of mass, and convex hull of the object, and about the smoothness, fundamental constraints, and periodicity of the 2-D Radon transform. The object is reconstructed using convolution backprojection applied to the estimated sinogram. We show several reconstructed objects which are obtained from simulated limited- and sparse-angle data using the described algorithm, and compare these results with images obtained using convolution backprojection directly.

AB - We present a method to reconstruct images from finite sets of noisy projections that may be available only over limited or sparse angles. The algorithm calculates the maximum a posteriori (MAP) estimate of the full sinogram (which is an image of the 2-D Radon transform of the object) from the available data. It is implemented using a primal-dual constrained optimization procedure that solves a partial differential equation in the primal phase with an efficient local relaxation algorithm and uses a simple Lagrange-multiplier update in the dual phase. The sinogram prior probability is given by a Markov random field (MRF) that includes information about the mass, center of mass, and convex hull of the object, and about the smoothness, fundamental constraints, and periodicity of the 2-D Radon transform. The object is reconstructed using convolution backprojection applied to the estimated sinogram. We show several reconstructed objects which are obtained from simulated limited- and sparse-angle data using the described algorithm, and compare these results with images obtained using convolution backprojection directly.

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U2 - 10.1016/0024-3795(90)90211-T

DO - 10.1016/0024-3795(90)90211-T

M3 - Article

AN - SCOPUS:0347582868

VL - 130

SP - 151

EP - 191

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - C

ER -