A Novel Tikhonov-Like Regularization Approach for the Applications of Inverse Radiation Analyzers Based on Prompt Gamma-Ray Neutron Activation Analysis
F. B. M. Silva1, S. B. Melo2, l. Meriç3, G. A. Johansen3, C. C. Dantas2, B. J. S. Barros1
1 Universidade Federal Rural de Pernambuco – Av. Bom Pastor, S/N-Boa Vista-Garanhuns-PE-Brazil.
2 Universidade Federal de Pernambuco – Av. Prof. Luis Freire, S/N – CDU-Recife-PE-Brazil.
3 Bergen University College – Inndalsveien 28 – Bergen – Norway. email@example.com
Unfolding of gamma-ray spectra is a very frequently encountered aspect of the research and development activities with focus on inverse radiation analyzers that have found applications within a variety of fields such as medicine, industry as well as homeland security. Recently, some works have been produced from investigating the applicability of inverse radiation analyzers based on Prompt Gamma-ray Neutron Activation Analysis (PGNAA) for subsea fluid characterization, by using Monte Carlo Library Least Squares (MCLLS), which consists of assuming a composition for the unknown object being investigated, and generating library spectra through accurate forward Monte Carlo (MC) simulations, while the amount of each pertinent library is calculated in a linear least-squares sense. This linear system, however, usually is “ill-conditioned”, exhibiting a high degree of sensitivity to small perturbations in the measurement data, thus leading to numerically unstable solutions. Previous approaches attempted to reduce this instability. Inspired by these works, we developed a new regularization method, based on a certain geometric modelling, which optimizes the MCLLS method through the proposal of aTikhonov-type regularization for mitigating the numerical instability. The technique hinges upon the production of barycentric coordinates out of the acquired libraries, which allows interpreting these libraries as vertices of triangles or other higher order simplexes. This also establishes a geometric framework with which one can model several relevant situations, such as how to identify geometrically what an adequate matrix conditioning means. In this work we present not only the construction of this framework but also some results that attest the applicability of this technique.
Keywords Compound-spanned Spaces, Monte Carlo Library Least Squares, PGNAA, Tikhonov Regularization, Subsea Fluid Characterization.
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