Monte-Carlo error analysis in x-ray spectral deconvolution
The deconvolution of spectral information from sparse x-ray data is a widely encountered problem in data analysis. An often-neglected aspect of this problem is the propagation of random error in the deconvolution process. We have developed a Monte-Carlo approach that enables us to attach error bars to unfolded x-ray spectra. Our Monte-Carlo error analysis has been incorporated into two specific deconvolution techniques: the first is an iterative convergent weight method; the second is a singular-value-decomposition (SVD) method. These two methods were applied to an x-ray spectral deconvolution problem having m channels of observations with n points in energy space. When m is less than n, this problem has no unique solution. We discuss the systematics of nonunique solutions and energy-dependent error bars for both methods. The Monte-Carlo approach has a particular benefit in relation to the SVD method: It allows us to apply the constraint of spectral nonnegativity after the SVD deconvolution rather than before. Consequently, we can identify inconsistencies between different detector channels.
- Research Organization:
- Applied Theoretical Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87544
- OSTI ID:
- 5761702
- Journal Information:
- Rev. Sci. Instrum.; (United States), Vol. 56:5
- Country of Publication:
- United States
- Language:
- English
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