Conference on Applied Inverse Problems, July 20-24, 2009, Vienna, Austria
Poster Presentation
Alexander Kharytonov: Regularized Solar Particle Spectra and Error Analysis for Measured Data from SOHO/EPHIN

Thu, 23 July, 2009, 17:15-18:15, Foyer

Joint work with E.Boehm and R.F.Wimmer-Schweingruber
(Institute of Experimental and Applied Physics, Kiel University, Germany).

The telescope EPHIN (Electron, Proton, Helium INstrument) on the SOHO
(SOlar and Heliosspheric Observatory) spacecraft measures the energy deposit
of solar particles passing through the detector system. The original energy
spectrum of solar particles is obtained by regularization methods from
EPHIN measurements. It is important not only to obtain the solution of this
inverse problem but also to estimate errors or uncertainties of the solution.
The basis of solar particle spectra calculation is the Fredholm integral
equation of the first kind with the instrument response function (IRF) as the
kernel which is obtained by the Monte Carlo technique in matrix form.
The original integral equation reduces to a singular system of linear
algebraic equations. The nonnegative solution is obtained by optimization
with constraints. For the starting value we use the solution of the algebraic
problem that is calculated by regularization methods such as the singular
value decomposition (SVD) or the Tikhonov methods.
We estimate the errors from special algebraic and statistical equations
that are considered as direct or inverse problems. Inverse problems for the
evaluation of errors are solved by regularization methods.
This inverse approach with error analysis is applied to data from the solar
particle event observed by SOHO/EPHIN on day 1996/191.
We have studied the impact of various error sources on the quantity of
uncertainties in the solution of the ill-posed problem. We considered errors
in the experimental data and the discrete forward operator or matrix.
In the error analysis we use well-known and newly developed methods,
such as the inverse problem for error propagation and the Monte Carlo method
with random perturbations in both the matrix and in measurement vector.
The error estimation obtained here correlates with the statistical accuracy
in both the observation vector and in the discrete forward operator (IRF).
We find that the various methods have different strengths and weaknesses in
the treatment of statistical and systematic errors.
Based on obtained results we claim that the Monte Carlo method with random
perturbations provides the best error estimation.

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