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Coded spectral X-ray computed tomography (CT) based on K-edge filtered illumination is a cost-effective approach to acquire both 3-dimensional structure of objects and their material composition. This approach allows sets of incomplete rays from sparse views or sparse rays with both spatial and spectral encoding to effectively reduce the inspection duration or radiation dose, which is of significance in biological imaging and medical diagnostics. However, reconstruction of spectral CT images from compressed measurements is a nonlinear and ill-posed problem. This paper proposes a material-decomposition-based approach to directly solve the reconstruction problem, without estimating the energy-binned sinograms. This approach assumes that the linear attenuation coefficient map of objects can be decomposed into a few basis materials that are separable in the spectral and space domains. The nonlinear problem is then converted to the reconstruction of the mass density maps of the basis materials. The dimensionality of the optimization variables is thus effectively reduced to overcome the ill-posedness. An alternating minimization scheme is used to solve the reconstruction with regularizations of weighted nuclear norm and total variation. Compared to the state-of-the-art reconstruction method for coded spectral CT, the proposed method can significantly improve the reconstruction quality. It is also capable of reconstructing the spectral CT images at two additional energy bins from the same set of measurements, thus providing more spectral information of the object.
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Combining Uneliminated Algebraic Formulations With Sparse Linear Solvers to Increase the Speed and Accuracy of Homotopy Path Tracking for Kinematic Synthesis
Abstract The method of kinematic synthesis requires finding the solution set of a system of polynomials. Parameter homotopy continuation is used to solve these systems and requires repeatedly solving systems of linear equations. For kinematic synthesis, the associated linear systems become ill-conditioned, resulting in a marked decrease in the number of solutions found due to path tracking failures. This unavoidable ill-conditioning places a premium on accurate function and matrix evaluations. Traditionally, variables are eliminated to reduce the dimension of the problem. However, this greatly increases the computational cost of evaluating the resulting functions and matrices and introduces numerical instability. We propose avoiding the elimination of variables to reduce required computations, increasing the dimension of the linear systems, but resulting in matrices that are quite sparse. We then solve these systems with sparse solvers to save memory and increase speed. We found that this combination resulted in a speedup of up to 250 × over traditional methods while maintaining the same accuracy.
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- Award ID(s):
- 2144732
- PAR ID:
- 10390975
- Date Published:
- Journal Name:
- Journal of Computing and Information Science in Engineering
- Volume:
- 22
- Issue:
- 6
- ISSN:
- 1530-9827
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4055241
