  This paper is concerned with the image reconstruction problem when the
measured data are solar hard X-ray modulation profiles obtained from the Reuven
Ramaty High Energy Solar Spectroscopic Imager (RHESSI)} instrument. Our goal is
to demonstrate that a statistical iterative method classically applied to the
image deconvolution problem is very effective when utilized for the analysis of
count modulation profiles in solar hard X-ray imaging based on Rotating
Modulation Collimators. The algorithm described in this paper solves the
maximum likelihood problem iteratively and encoding a positivity constraint
into the iterative optimization scheme. The result is therefore a classical
Expectation Maximization method this time applied not to an image deconvolution
problem but to image reconstruction from count modulation profiles. The
technical reason that makes our implementation particularly effective in this
application is the use of a very reliable stopping rule which is able to
regularize the solution providing, at the same time, a very satisfactory
Cash-statistic (C-statistic). The method is applied to both reproduce synthetic
flaring configurations and reconstruct images from experimental data
corresponding to three real events. In this second case, the performance of
Expectation Maximization, when compared to Pixon image reconstruction, shows a
comparable accuracy and a notably reduced computational burden; when compared
to CLEAN, shows a better fidelity with respect to the measurements with a
comparable computational effectiveness. If optimally stopped, Expectation
Maximization represents a very reliable method for image reconstruction in the
RHESSI context when count modulation profiles are used as input data.
