We use L1-norm model regularization of |Br| component at the surface on magnetic monopoles bases and along-track magnetic field differences alone (without vector observations) to derive high quality global magnetic field models at the surface of the Moon. The practical advantages to this strategy are: monopoles are more stable at closer spacing in comparison to dipoles, improving spatial resolution; L1-norm model regularization leads to sparse models which may be appropriate for the Moon which has regions of localized magnetic field features; and along-track differences reduce the need for ad-hoc external field noise reduction strategies. We examine also the use of Lunar Prospector (LP) and SELENE/Kaguya magnetometer data, combined and separately, and find that the LP alongtrack vector field differences lead to surface field models that require weaker regularization and, hence, result in higher spatial resolution. Significantly higher spatial resolution (wavelengths of roughly 25-30 km) and higher amplitude surface magnetic fields can be derived over localized regions of high amplitude anomalies (due to their higher signal-tonoise ratio). These high resolution field models are also compared with the results of Surface Vector Mapping (SVM) approach of Tsunakawa et al. (2015). Finally, the monopoles- as well as dipoles-based patterns of the Serenitatis high amplitude magnetic feature have characteristic textbook patterns of Br and B component fields from a nearly vertically downwardly magnetized source region and it implies that the principal source of the anomaly was formed when the region was much closer to the north magnetic pole of the Moon.