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We describe a "spatio-spectral" deconvolution algorithm for wide-band imagingin radio interferometry. In contrast with the existing multi-frequencyreconstruction algorithms, the proposed method does not rely on a model of thesky-brightness spectral distribution. This non-parametric approach can be ofparticular interest for the new generation of low frequency radiotelescopes.The proposed solution formalizes the reconstruction problem as a convexoptimization problem with spatial and spectral regularizations. The efficiencyof this approach has been already proven for narrow-band image reconstructionand the present contribution can be considered as its extension to themulti-frequency case. Because the number of frequency bands multiplies the sizeof the inverse problem, particular attention is devoted to the derivation of aniterative large scale optimization algorithm. It is shown that the maincomputational bottleneck of the approach, which lies in the resolution of alinear system, can be efficiently overcome by a fully parallel implementationw.r.t. the frequencies, where each processor reconstructs a narrow-band image.All the other optimization steps are extremely fast. A parallel implementationof the algorithm in Julia is publicly available athttps://github.com/andferrari. Preliminary simulations illustrate theperformances of the method and its ability to reconstruct complexspatio-spectral structures.

Multi-frequency image reconstruction for radio interferometry. A regularized inverse problem approach