Inverse transport problem solvers based on regularized and compressive sensing techniques

Title: Inverse transport problem solvers based on regularized and compressive sensing techniques

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Abstract

According to the direct exposure measurements from flash radiographic image, regularized-based method and compressive sensing (CS)-based method for inverse transport equation are presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. With a large number of measurements, least-square method is utilized to complete the reconstruction. Owing to the ill-posedness of the inverse problems, regularized algorithm is employed. Tikhonov method is applied with an appropriate posterior regularization parameter to get a meaningful solution. However, it's always very costly to obtain enough measurements. With limited measurements, CS sparse reconstruction technique Orthogonal Matching Pursuit (OMP) is applied to obtain the sparse coefficients by solving an optimization problem. This paper constructs and takes the forward projection matrix rather than Gauss matrix as measurement matrix. In the CS-based algorithm, Fourier expansion and wavelet expansion are adopted to convert an underdetermined system to a well-posed system. Simulations and numerical results of regularized method with appropriate regularization parameter and that of CS-based agree well with the reference value, furthermore, both methods avoid amplifying the noise. (authors)

Authors:

Cheng, Y.; Cao, L.; Wu, H.; Zhang, H. ^[1]

School of Nuclear Science and Technology, Xi'an Jiaotong Univ., Xianning West Road No.28, Xi'an, Shaanxi, 710049 (China)

Publication Date:: 2012-07-01

Research Org.:: American Nuclear Society, Inc., 555 N. Kensington Avenue, La Grange Park, Illinois 60526 (United States)

OSTI Identifier:: 22105840

Resource Type:: Conference

Resource Relation:: Conference: PHYSOR 2012: Conference on Advances in Reactor Physics - Linking Research, Industry, and Education, Knoxville, TN (United States), 15-20 Apr 2012; Other Information: Country of input: France; 17 refs.

Country of Publication:: United States

Language:: English

Subject:: 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 22 GENERAL STUDIES OF NUCLEAR REACTORS; ALGORITHMS; APPROXIMATIONS; EXPANSION; IMAGES; LEAST SQUARE FIT; MATRICES; OPTIMIZATION; SENSORS; SIGNALS; SIMULATION; TRANSPORT THEORY

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                    Cheng, Y., Cao, L., Wu, H., and Zhang, H. Inverse transport problem solvers based on regularized and compressive sensing techniques.  United States: N. p., 2012. 
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                    Cheng, Y., Cao, L., Wu, H., & Zhang, H. Inverse transport problem solvers based on regularized and compressive sensing techniques.  United States.

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                    Cheng, Y., Cao, L., Wu, H., and Zhang, H. Sun .  
        "Inverse transport problem solvers based on regularized and compressive sensing techniques".  United States.

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@article{osti_22105840,

  title        = {Inverse transport problem solvers based on regularized and compressive sensing techniques},

  author       = {Cheng, Y. and Cao, L. and Wu, H. and Zhang, H.},

  abstractNote = {According to the direct exposure measurements from flash radiographic image, regularized-based method and compressive sensing (CS)-based method for inverse transport equation are presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. With a large number of measurements, least-square method is utilized to complete the reconstruction. Owing to the ill-posedness of the inverse problems, regularized algorithm is employed. Tikhonov method is applied with an appropriate posterior regularization parameter to get a meaningful solution. However, it's always very costly to obtain enough measurements. With limited measurements, CS sparse reconstruction technique Orthogonal Matching Pursuit (OMP) is applied to obtain the sparse coefficients by solving an optimization problem. This paper constructs and takes the forward projection matrix rather than Gauss matrix as measurement matrix. In the CS-based algorithm, Fourier expansion and wavelet expansion are adopted to convert an underdetermined system to a well-posed system. Simulations and numerical results of regularized method with appropriate regularization parameter and that of CS-based agree well with the reference value, furthermore, both methods avoid amplifying the noise. (authors)},

  doi          = {},

  url          = {https://www.osti.gov/biblio/22105840},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {2012},

  month        = {7}

}

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