With the advent of the next-generation radio-interferometric telescopes, like the Square Kilometre Array, novel signal processing methods are needed to provide the expected imaging resolution and sensitivity from extreme amounts of hyper-spectral data. In this context, we propose a generic non-parametric low-rank and joint-sparsity image model for the regularisation of the associated wide-band inverse problem. We pose a convex optimisation problem and propose the use of an efficient algorithmic solver. The proposed optimisation task requires only one tuning parameter, namely the relative weight between the low-rank and joint-sparsity constraints. Our preliminary simulations suggest superior performance of the model with respect to separate single band imaging, as well as to other recently promoted non-parametric wide-band models leveraging convex optimisation.