  In this paper we present new optimization strategies for the reconstruction
of X-ray images of solar flares by means of the data collected by the Reuven
Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The imaging concept of
the satellite is based of rotating modulation collimator instruments, which
allow the use of both Fourier imaging approaches and reconstruction techniques
based on the straightforward inversion of the modulated count profiles.
Although in the last decade a greater attention has been devoted to the former
strategies due to their very limited computational cost, here we consider the
latter model and investigate the effectiveness of different accelerated
gradient methods for the solution of the corresponding constrained minimization
problem. Moreover, regularization is introduced through either an early
stopping of the iterative procedure, or a Tikhonov term added to the
discrepancy function, by means of a discrepancy principle accounting for the
Poisson nature of the noise affecting the data.
