We introduce Global Positioning System (GPS) Imaging, a new technique for robust estimation of the vertical velocity field of the Earth's surface, and apply it to the Sierra Nevada Mountain range in the western United States. Starting with vertical position time series from Global Positioning System (GPS) stations, we first estimate vertical velocities using the MIDAS robust trend estimator, which is insensitive to undocumented steps, outliers, seasonality, and heteroscedasticity. Using the Delaunay triangulation of station locations, we then apply a weighted median spatial filter to remove velocity outliers and enhance signals common to multiple stations. Finally, we interpolate the data using weighted median estimation on a grid. The resulting velocity field is temporally and spatially robust and edges in the field remain sharp. Results from data spanning 5-20years show that the Sierra Nevada is the most rapid and extensive uplift feature in the western United States, rising up to 2mm/yr along most of the range. The uplift is juxtaposed against domains of subsidence attributable to groundwater withdrawal in California's Central Valley. The uplift boundary is consistently stationary, although uplift is faster over the 2011-2016 period of drought. Uplift patterns are consistent with groundwater extraction and concomitant elastic bedrock uplift, plus slower background tectonic uplift. A discontinuity in the velocity field across the southeastern edge of the Sierra Nevada reveals a contrast in lithospheric strength, suggesting a relationship between late Cenozoic uplift of the southern Sierra Nevada and evolution of the southern Walker Lane.