The key aspect of the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is its ability to produce X-ray images in different energy bands [5] and so to determine the hard X-ray spectrum at different locations. Instrumentally, RHESSI collimators realize this capability indirectly, inasmuch X-ray images are synthesized by applying back-projection/reconstruction algorithms and X-ray spectroscopy requires spectral deconvolution in order to reduce the detector response. Furthermore, on a more physical level, deconvolved, spatially integrated X-ray spectra must be inverted to reconstruct spatially integrated electron spectra and therefore to gain first insights about the acceleration mechanisms in solar plasma during flares.

Our previous project, funded by ISSI for the period 2005-2006, was focused on the formulation and application of inversion methods [4,9] for the restoration of mean electron spectra from RHESSI X-ray spectra. The main results of this activity have been the validation and comparison of different regularization methods in the reconstruction of the mean electron spectrum from X-ray data [1,2,6,7] and the implementation of one of these methods into an IDL code which is being integrated in the official Solar SoftWare (SSW) for the mission data analysis and which provides RHESSI (and even non-RHESSI) community of a powerful data analysis tool not previously available. Other results in the framework of this first project have been the study of the influence of albedo [6] and electron-electron bremsstrahlung contribution on X-ray solar spectroscopy and the formulation of a reconstruction method for the differential emission measure from X-ray spectra in a thermal interpretation of the bremsstrahlung emission process [8].

As far as the problem of image construction from raw RHESSI data, our results have been so far exploratory, and form the base for the current proposal.

[1] Brown J.C., Emslie A.G., Holman G.D., Johns-Krull C.M., Kontar E.P., Lin R.P., Massone A.M. and Piana M., 2006, Evaluation of algorithms for reconstructing electron spectra from their bremsstrahlung hard X-ray spectra. ApJ, in press.

[3] Brown, J.C., Kontar, E.P., and Veronig, A.M., 2006, RHESSI Results - Time For a Rethink, Lecture Notes of Physics, Springer, submitted

[4] Craig, I. J. D. & Brown, J. C., 1986, Inverse Problems in Astronomy, Adam Hilger, London.

[5] Hurford G.J. et al., 2002, The RHESSI Imaging Concept. Sol. Phys. 210, 61-86.

[6] Kašparová, J., Karlický, M., Kontar, E.P., Schwartz, R.A. and Dennis, B.R., 2005, Multi-Wavelength Analysis of High-Energy Electrons in Solar Flares: a Case Study of the August 20, 2002 Flare, Sol. Phys. 232, 63.

[7] Massone, A. M., Brown, J.C., Emslie, A. G., Kontar, E. P., Piana, M. and Prato, M. 2006, Bremsstrahlung emission during solar flares: reconstruction of the electron spectra by means of inversion methods and applications to RHESSI data, Memorie della Società Astronomica Italiana, in press.

[9] Tikhonov A.N., 1963, On solving ill-posed problems and method of regularization Dokl. Akad. Nauk. USSR 153, 501-504.