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Maximum a posteriori technique applied to energy‐dispersive X‐ray fluorescence spectra
Author(s) -
Schwalbe L. A.,
Trussell H. J.
Publication year - 1981
Publication title -
x‐ray spectrometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 45
eISSN - 1097-4539
pISSN - 0049-8246
DOI - 10.1002/xrs.1300100409
Subject(s) - a priori and a posteriori , deconvolution , formalism (music) , maximum a posteriori estimation , spectral line , consistency (knowledge bases) , maximum likelihood , energy (signal processing) , energy spectrum , spectrum (functional analysis) , mathematics , statistical physics , physics , algorithm , statistics , quantum mechanics , discrete mathematics , art , musical , philosophy , epistemology , visual arts
We review the maximum a posteriori formalism and apply the technique to the deconvolution problem of energy‐dispsersive X‐ray fluorescence spectra. An exact closed‐from expression for the a priori probability density is derived from physical considerations. A single CuZn spectrum is taken to illustrate the effects of various assumed forms for the restored spectrum probability distributions. Our best results follow from calculations that involve a self‐consistency condition. These restorations are contained within the set of maximum likelihood solutions.