A major factor that prevents the large scale deployment of Mobile Crowd Sensing (MCS) is its sensing and communication cost. Given the spatio-temporal correlation among the environment monitoring data, matrix completion (MC) can be exploited to only monitor a small part of locations and time, and infer the remaining data. Rather than only taking random measurements following the basic MC theory, to further reduce the cost of MCS while ensuring the quality of missing data inference, we propose an Active Sparse MCS (AS-MCS) scheme which includes a bipartite-graph-based sensing scheduling scheme to actively determine the sampling positions in each upcoming time slot, and a bipartite-graph-based matrix completion algorithm to robustly and accurately recover the un-sampled data in the presence of sensing and communications errors. We also incorporate the sensing cost into the bipartite-graph to facilitate low cost sample selection and consider the incentives for MCS. We have conducted extensive performance studies using the data sets from the monitoring of PM 2.5 air condition and road traffic speed, respectively. Our results demonstrate that our AS-MCS scheme can recover the missing data at very high accuracy with the sampling ratio only around 11%, while the peer matrix completion algorithms with similar recovery performance requires up to 4-9 times the number of samples of ours for both the data sets.