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Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, eg object detection, classification, tracking of multiple agents, or denoising, to name a few. The key idea is that exploring task relatedness (structure) can lead to better performances. In this paper, we propose and study a novel sparse, non-parametric approach exploiting the theory of Reproducing Kernel Hilbert Spaces for vector-valued functions. We develop a suitable regularization framework which can be formulated as a convex optimization problem, and is provably solvable using an alternating minimization approach. Empirical tests show that the proposed method compares favorably to state of the art techniques and further allows to recover interpretable structures, a problem of interest in its own right.