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P. Charbonneau, S. McIntosh (HAO/NCAR)
In an inverse problem of any kind, poor conditioning of the inverse operator decreases the numerical stability of any unregularized solution in the presence of data noise. In this poster we show that the numerical stability of the differential emission measure (DEM) inverse problem can be considreably improved by judicious choice of the integral operator. Specifically, we formulate a combinatorial optimization problem where, in a preconditioning step, a subset of spectral lines is selected in order to minimize the condition number of the discretized integral operator. This turns out to be a hard combinatorial optimization problem, which we tackle using a genetic algorithm.
We apply the technique to the dataset comprising the solar UV/EUV emission lines in the SOHO SUMER/CDS wavelength range, and to the Harvard S-055 EUV spectroheliometer data. The temperature distribution in the emitting region of the solar atmosphere is recovered with considerably better stability and smaller error bars when our preconditioning technique is used, even though this involves the analysis of fewer spectral lines than in the conventional ``all-lines'' approach.
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