Estimates of soil moisture and surface salinity are of significant importance to improve meteorological and climate prediction. The SMOS mission monitor these quantities, by measuring the brightness temperature by means of L-band aperture synthesis interferometry. Despite the L-band being reserved for Earth and space exploration, SMOS images reveal large number of strong outliers, produced by illegal antennas emitting in this band. In this work we propose a variational approach to recover a super-resolved, denoised brightness temperature map. The measurements are modeled as the superposition of three super-resolved components in the spatial domain: the target brightness temperature map u, an image o modeling the outliers, and Gaussian noise n. This decomposition allows to isolate each of its constituent parts, thanks to a sparsity operator that acts on o, and a bounded variation prior on u that extrapolates its spectrum promoting a non-oscillating behavior. The proposed model is interesting in itself, as it is general enough to be applied to other restoration problems. Experiments on real and synthetic data confirm the suitability of the proposed approach.