Purpose Several parallel transmit MRI techniques require knowledge of the transmit radiofrequency field profiles (B sub(1) super(+)). During the past years, various methods have been developed to acquire this information. Often, these methods suffer from long measurement times and produce maps exhibiting regions with poor signal-to-noise ratio and artifacts. In this article, a model-based reconstruction procedure is introduced that improves the robustness of B sub(1) super(+) mapping. Theory and Methods The missing information from undersampled B sub(1) super(+) maps and the regions of poor signal to noise ratio are reconstructed through projection into the space of spherical functions that arise naturally from the solution of the Helmholtz equations in the spherical coordinate system. Results As a result, B sub(1) super(+) data over a limited range of the field of view/volume is sufficient to reconstruct the B sub(1) super(+) over the full spatial domain in a fast and robust way. The same model is exploited to filter the noise of the measured maps. Results from simulations and in vivo measurements confirm the validity of the proposed method. Conclusion A spherical functions model can well approximate the magnetic fields inside the body with few basis terms. Exploiting this compression capability, B sub(1) super(+) maps are reconstructed in regions of unknown or corrupted values. Magn Reson Med 71:394-401, 2014. copyright 2013 Wiley Periodicals, Inc.