Robust construction of differential emission measure profiles using a regularized maximum likelihood method

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Table 1

Metrics for the single Gaussian “ground truth” model test.

Method	log₁₀ Tc = 6.1			log₁₀ T_c = 6.2			log₁₀ T_c = 6.3			log₁₀ T_c = 6.4

	Red. χ²	NRMSE Mean	NRMSE Std. Dev.	Red. χ²	NRMSE Mean	NRMSE Std. Dev.	Red. χ²	NRMSE Mean	NRMSE Std. Dev.	Red. χ²	NRMSE Mean	NRMSE Std. Dev.
BP	6.7 ± 1.2	0.10	0.01	7.8 ± 1.1	0.19	0.04	6.1 ± 1.8	0.48	0.16	6.7 ± 0.9	1.22	0.01
FIR	2.5 ± 1.1	0.55	0.06	1.8±1.3	0.54	0.05	2.0±1.4	0.81	0.06	2.5±1.4	1.29	0.02
SITES	2.7±1.2	0.70	0.05	2.2±1.6	0.60	0.07	0.9 ± 1.1	0.24	0.05	0.8 ± 0.7	0.47	0.13
REG	45 ± 14	0.42	0.04	41 ± 14	0.49	0.06	27 ± 23	0.83	0.14	9.9±15	1.27	0.08
ML	2.7 ± 1.1	0.61	0.09	2.4±1.3	0.50	0.11	2.2±1.5	0.42	0.07	1.2±1.2	0.37	0.07
RML	1.9±1.5	0.48	0.04	1.6±1.6	0.44	0.05	1.4±1.5	0.87	0.01	1.0 ± 0.6	1.41	0.09

Notes. The rows represent the six different reconstruction methods used (see text), while the columns are labeled by the (logarithm of the) centroid temperature of the Gaussian. For each case, the column “Red. χ²” is the mean ± standard deviation of the reduced χ² values over the 25 different realizations of the simulated data, while the next two columns measure the mean of the normalized root mean square error between the 25 recovered ξ(T) profiles (a measure of the accuracy of the recovered profile) and its standard deviation (a measure of the robustness of the recovered profile to the introduction of data noise).

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