EXAFS Phase Retrieval Solution Tracking for Complex Multi-Component System: Synthesized Topological Inverse Computation

Using the FEFF kernel A(k,r), we describe the inverse computation from χ(k)-data to g(r)-solution in terms of a singularity regularization method based on complete Bayesian statistics process. In this work, we topologically decompose the system-matched invariant projection operators into two distinc...

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Bibliographic Details
Published in:Journal of physics. Conference series 2013-01, Vol.430 (1), p.12013-4
Main Authors: Lee, Jay Min, Yang, Dong-Seok, Bunker, Grant B
Format: Article
Language:English
Subjects:
Computation
Emulators
Invariants
Inverse
Mathematical models
Optimization
Phase retrieval
Physics
Regularization
Regularization methods
Synthesis
Topology
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Summary:Using the FEFF kernel A(k,r), we describe the inverse computation from χ(k)-data to g(r)-solution in terms of a singularity regularization method based on complete Bayesian statistics process. In this work, we topologically decompose the system-matched invariant projection operators into two distinct types, (A+AA+A) and (AA+AA+), and achieved Synthesized Topological Inversion Computation (STIC), by employing a 12-operator-closed-loop emulator of the symplectic transformation. This leads to a numerically self-consistent solution as the optimal near-singular regularization parameters are sought, dramatically suppressing instability problems connected with finite precision arithmetic in ill-posed systems. By statistically correlating a pair of measured data, it was feasible to compute an optimal EXAFS phase retrieval solution expressed in terms of the complex-valued χ(k), and this approach was successfully used to determine the optimal g(r) for a complex multi-component system.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/430/1/012013