We present a method for imaging the global crustal magnetic field at Earth's surface using a local basis representation and a minimum norm model regularization approach. The local basis consists of a spherical triangle tessellation (STT) parametrization of the radial component of the crustal field at Earth's reference spherical surface. The Green's function for Laplace's equation in spherical geometry with Neumann boundary conditions provides the necessary forward modelling scheme. We solve the inverse problem of estimating the crustal field from satellite magnetic observations by minimizing an objective function comprising a mean absolute deviation (L1-norm) measure of misfit plus a norm measuring model complexity. Both quadratic and entropy measures of field complexity are investigated. We report results from synthetic tests performed on a geophysically motivated scenario; these include a successful benchmark of the method and a comparison between quadratic and entropy regularization strategies. Applying our technique to real observations collected by the CHAMP, Ørsted and SAC-C satellites, we obtain stable images of the crustal magnetic field at Earth's surface that include sharp features with high amplitudes. We present details of two prototype crustal field models STT-CRUST-Q and STT-CRUST-E regularized using quadratic and entropy norms respectively; these provide a perspective complementary to that given by conventional spherical harmonic crustal field model
