  We describe a "spatio-spectral" deconvolution algorithm for wide-band imaging
in radio interferometry. In contrast with the existing multi-frequency
reconstruction algorithms, the proposed method does not rely on a model of the
sky-brightness spectral distribution. This non-parametric approach can be of
particular interest for the new generation of low frequency radiotelescopes.
The proposed solution formalizes the reconstruction problem as a convex
optimization problem with spatial and spectral regularizations. The efficiency
of this approach has been already proven for narrow-band image reconstruction
and the present contribution can be considered as its extension to the
multi-frequency case. Because the number of frequency bands multiplies the size
of the inverse problem, particular attention is devoted to the derivation of an
iterative large scale optimization algorithm. It is shown that the main
computational bottleneck of the approach, which lies in the resolution of a
linear system, can be efficiently overcome by a fully parallel implementation
w.r.t. the frequencies, where each processor reconstructs a narrow-band image.
All the other optimization steps are extremely fast. A parallel implementation
of the algorithm in Julia is publicly available at
https://github.com/andferrari. Preliminary simulations illustrate the
performances of the method and its ability to reconstruct complex
spatio-spectral structures.
