  Maximum Entropy is an image reconstruction method conceived to image a
sparsely occupied field of view and therefore particularly appropriate to
achieve super-resolution effects. Although widely used in image deconvolution,
this method has been formulated in radio astronomy for the analysis of
observations in the spatial frequency domain, and an Interactive Data Language
(IDL) code has been implemented for image reconstruction from solar X-ray
Fourier data. However, this code relies on a non-convex formulation of the
constrained optimization problem addressed by the Maximum Entropy approach and
this sometimes results in unreliable reconstructions characterized by
unphysical shrinking effects.
  This paper introduces a new approach to Maximum Entropy based on the
constrained minimization of a convex functional. In the case of observations
recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI),
the resulting code provides the same super-resolution effects of the previous
algorithm, while working properly also when that code produces unphysical
reconstructions. Results are also provided of testing the algorithm with
synthetic data simulating observations of the Spectrometer/Telescope for
Imaging X-rays (STIX) in Solar Orbiter. The new code is available in the
{\em{HESSI}} folder of the Solar SoftWare (SSW)tree.
