Compression Schemes for Time-Varying Sparse Signals

Abstract—In this paper, we will investigate an adaptive com-pression scheme for tracking time-varying sparse signals with possibly varying sparsity patterns and/or order. In particular, we will focus on sparse sensing, which enables a completely distributed compression and simplifies the sampling architecture. The sensing matrix is designed at each time step based on the entire history of measurements and known dynamics such that the information gain is maximized. We illustrate the developed theory with a target tracking example. Finally, we provide a few extensions of the proposed framework to include a richer class of sparse signals, e.g., structured sparsity and smoothness. Index Terms—Structured sensing, sensor selection, sparsity-aware Kalman filter, sparse sensing, adaptive compressed sensing, distributed compression, big data. I