  Sparse inpainting techniques are gaining in popularity as a tool for
cosmological data analysis, in particular for handling data which present
masked regions and missing observations. We investigate here the relationship
between sparse inpainting techniques using the spherical harmonic basis as a
dictionary and the isotropy properties of cosmological maps, as for instance
those arising from cosmic microwave background (CMB) experiments. In
particular, we investigate the possibility that inpainted maps may exhibit
anisotropies in the behaviour of higher-order angular polyspectra. We provide
analytic computations and simulations of inpainted maps for a Gaussian
isotropic model of CMB data, suggesting that the resulting angular trispectrum
may exhibit small but non-negligible deviations from isotropy.
