Learning Compressive Sensing Models for Big Spatio-Temporal Data

Abstract

Sensing devices including mobile phones and biomedical sensors generate massive amounts of spatio-temporal data. Compressive sensing (CS) can significantly reduce energy and resource consumption by shifting the complexity burden of encoding process to the decoder. CS reconstructs the compressed signals exactly with overwhelming probability when incoming data can be sparsely represented with a fixed number of components, which is one of drawbacks of CS frameworks because a real-world signal in general cannot be represented with the fixed number of components. We present the first CS framework that handles signals without the fixed sparsity assumption by incorporating the distribution of the number of principal components included in the signal recovery, which we show is naturally represented by the gamma distribution. This allows an analytic derivation of total error in our spatio-temporal Low Complexity Sampling (LCS). We show that LCS requires shorter compressed signals than existing CS frameworks to bound the same amount of error. Experiments with real-world sensor data also demonstrate that LCS outperforms existing CS frameworks.