Participatory sensing enables to collect a vast amount of data from the crowd by allowing a wide variety of sources to contribute data. However, the openness of participatory sensing exposes the system to malicious and erroneous participations, inevitably resulting in poor data quality. This brings forth the important issues of false data detection and correction in participatory sensing. Furthermore, data collected by participants normally include considerable missing values, which poses challenges for accurate false data detection. In this work, we propose DECO, a general framework to detect false values for participatory sensing in the presence of missing data. By applying a tailored spatio-temporal compressive sensing technique, DECO is able to accurately detect the false data and estimate both false and missing values for data correction. We validate our design through an experimental case study.