In the present proposal we address the core problem of combining high-resolution imaging in hard X-rays with high-resolution spectroscopy (imaging spectroscopy). Although this project is intended as a comprehensive and complete investigation through RHESSI data that stands on its own scientific merits, it also represents the first step toward a new vision of the regularization process in a 3D space characterized by one spectral and two spatial dimensions. The end products will consist of:

• further development of algorithms and software for analysis of RHESSI spectra and images;

• use of the new software inversion package for imaging spectroscopy;

• publication of papers in international refereed journals in the domains of Astronomy, Astrophysics, Numerical Analysis, Applied Mathematics and Computer Science;

• presentation of the results obtained during international conferences in these multidisciplinary fields;

• maintenance of our team web page (http://www.issibern.ch/teams/invermethod/) with an up-to-date description of the team activity, links to other relevant web pages, and the ability to download preprints, reports and software.