Understanding human mobility is of vital importance for urban planning, epidemiology, and many other fields that draw policies from the activities of humans in space. Despite the recent availability of large-scale data sets of GPS traces or mobile phone records capturing human mobility, typically only a subsample of the population of interest is represented, giving a possibly incomplete picture of the entire system under study. Methods to reliably extract mobility information from such reduced data and to assess their sampling biases are lacking. To that end, we analyzed a data set of millions of taxi movements in New York City. We first show that, once they are appropriately transformed, mobility patterns are highly stable over long time scales. Based on this observation, we develop a supersampling methodology to reliably extrapolate mobility records from a reduced sample based on an entropy maximization procedure, and we propose a number of network-based metrics to assess the accuracy of the predicted vehicle flows. Our approach provides a well founded way to exploit temporal patterns to save effort in recording mobility data, and opens the possibility to scale up data from limited records when information on the full system is required.