  The paper deals with the construction of images from visibilities acquired
using aperture synthesis instruments: Fourier synthesis, deconvolution, and
spectral interpolation/extrapolation. Its intended application is to specific
situations in which the imaged object possesses two superimposed components:
($i$) an extended component together with ($ii$) a set of point sources. It is
also specifically designed to the case of positive maps, and accounts for a
known support. Its originality lies within joint estimation of the two
components, coherently with data, properties of each component, positivity and
possible support. We approach the subject as an inverse problem within a
regularization framework: a regularized least-squares criterion is specifically
proposed and the estimated maps are defined as its minimizer. We have
investigated several options for the numerical minimization and we propose a
new efficient algorithm based on augmented Lagrangian. Evaluation is carried
out using simulated and real data (from radio interferometry) demonstrating the
capability to accurately separate the two components.
