  The Richardson-Lucy method is the most popular deconvolution method in
astronomy because it preserves the number of counts and the non-negativity of
the original object. Regularization is, in general, obtained by an early
stopping of Richardson-Lucy iterations. In the case of point-wise objects such
as binaries or open star clusters, iterations can be pushed to convergence.
However, it is well-known that Richardson-Lucy is an inefficient method. In
most cases, acceptable solutions are obtained at the cost of hundreds or
thousands of iterations. A general optimization method, referred to as the
scaled gradient projection method, has been proposed for the constrained
minimization of continuously differentiable convex functions. It is applicable
to the non-negative minimization of the Kullback-Leibler divergence. If the
scaling suggested by Richardson-Lucy is used in this method, then it provides a
considerable increase in the efficiency of Richardson-Lucy. Therefore the aim
of this paper is to apply the scaled gradient projection method to a number of
imaging problems in astronomy such as single image deconvolution, multiple
image deconvolution, and boundary effect correction. The corresponding
algorithms are derived and implemented in interactive data language. To attempt
to achieve a further increase in efficiency, we also consider an implementation
on graphic processing units. The proposed algorithms are tested on simulated
images. The acceleration of scaled gradient projection methods achieved with
respect to the corresponding Richardson-Lucy methods strongly depends on both
the problem and the specific object to be reconstructed, and in our simulations
the improvement achieved ranges from about a factor of 4 to more than 30.
Moreover, significant accelerations of up to two orders of magnitude have been
observed between the serial and parallel implementations of the algorithms.
