A method and apparatus for spatio-temporal compressive sensing, which allows accurate reconstruction of missing values in any digital information represented in matrix or tensor form, is disclosed. The method of embodiments comprises three main components: (i) a method for finding sparse, low-rank approximations of the data of interest that account for spatial and temporal properties of the data, (ii) a method for finding a refined approximation that better satisfies the measurement constraints while staying close to the low-rank approximations obtained by SRMF, and (iii) a method for combining global and local interpolation. The approach of embodiments also provides methods to perform common data analysis tasks, such as tomography, prediction, and anomaly detection, in a unified fashion.