Regularization Methods for the recovery of the differential emission 
measure from RHESSI X-ray spectra.
The problem of determining the differential emission measure in the solar 
plasma from measures of hard X-ray spectra can be modelled as the problem 
of inverting a real Laplace Transform. This linear inverse problem is 
extremely ill-posed, which implies that the presence of noise in the 
measured data is reflected into strong numerical instabilities when the 
inversion procedure is performed in a naive way. In order to reduce this 
ill-conditioning, a possible approach is to apply the Tikhonov 
regularization method, where the penalty term provides a bound on the 
first derivative of the regularized differential emission measure. We 
apply this approach to different RHESSI spectra, using a careful analysis 
of the residuals in order to optimally fix the value of the regularization 
parameter.