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Inverse problems are of great importance in astrophysics for derivinginformation about the physical characteristics of hot optically thin plasmasources from their EUV and X-ray spectra. We describe and test an iterativemethod developed within the framework of a probabilistic approach to thespectral inverse problem for determining the thermal structures of the emittingplasma. We also demonstrate applications of this method to both high resolutionline spectra and broadband imaging data. Our so-called Bayesian iterativemethod (BIM) is an iterative procedure based on Bayes' theorem and is used toreconstruct differential emission measure (DEM) distributions. To demonstratethe abilities of the BIM, we performed various numerical tests and modelsimulations establishing its robustness and usefulness. We then applied the BIMto observable data for several active regions (AR) previously analyzed withother DEM diagnostic techniques: both SUMER/SOHO (Landi and Feldman, 2008) andSPIRIT/CORONAS-F (Shestov et al., 2010) line spectra data, and XRT/Hinode(Reale et al., 2009) broadband imaging data. The BIM results show that thismethod is an effective tool for determining the thermal structure of emittingplasma and can be successfully used for the DEM analysis of both line spectraand broadband imaging data. The BIM calculations correlate with recent studiesconfirming the existence of hot plasma in solar ARs. The BIM results alsoindicate that the coronal plasma may have the continuous distributionspredicted by the nanoflare paradigm.

An iterative method in a probabilistic approach to the spectral inverse problem: Differential emission measure from line spectra and broadband data