Differential Emission Measures from the Regularized Inversion of Hinode and SDO data

We develop and apply an enhanced regularization algorithm, used in RHESSI X-ray spectral analysis, to constrain the ill-posed inverse problem that is determining the DEM from solar observations. We demonstrate this computationally fast technique applied to a range of DEM models simulating broadband imaging data from SDO/AIA and high resolution line spectra from Hinode/EIS, as well as actual active region observations with Hinode/EIS and XRT. As this regularization method naturally provides both vertical and horizontal (temperature resolution) error bars we are able to test the role of uncertainties in the data and response functions. The regularization method is able to successfully recover the DEM from simulated data of a variety of model DEMs (single Gaussian, multiple Gaussians and CHIANTI DEM models). It is able to do this, at best, to over four orders of magnitude in DEM space but typically over two orders of magnitude from peak emission. The combination of horizontal and vertical error bars and the regularized solution matrix allows us to easily determine the accuracy and robustness of the regularized DEM. We find that the typical range for the horizontal errors is $Delta$log$Tapprox 0.1 -0.5$ and this is dependent on the observed signal to noise, uncertainty in the response functions as well as the source model and temperature. With Hinode/EIS an uncertainty of 20% greatly broadens the regularized DEMs for both Gaussian and CHIANTI models although information about the underlying DEMs is still recoverable. When applied to real active region observations with Hinode/EIS and XRT the regularization method is able to recover a DEM similar to that found via a MCMC method but in considerably less computational time.