Solar flares are the most explosive phenomena in the
heliosphere, producing huge amounts of energy in a few seconds with an
 impressive electromagnetic emission at all wavelengths. It has been
 recognized since the early days of space investigation that high-energy
 observations play a crucial role in understanding the basic mechanisms of
 these solar eruptions. Unfortunately, the peculiar nature of this radiation
 makes it so difficult to extract useful information from it that
 nonconventional observational techniques together with complex data
 analysis procedures must be adopted. Specifically, regularization theory
 for the solution of ill-posed inverse problems allows the reconstruction of
 images of these events whose pixel content is proportional to the quantity
 of matter, specifically electrons, accelerated in the flaring atmosphere.
 These electron maps can be utilized to validate PDE-based models of the
 emission mechanisms and to experimentally estimate some crucial physical
 parameters in the flaring target.