Sparse Sensing for Statistical Inference

Abstract

In today’s society, we are flooded with massive volumes of data in the order of a billion gigabytes on a daily basis from pervasive sensors. It is becoming increasingly challenging to sense, store, transport, or process (i.e., for inference) the acquired data. To alleviate these problems, it is evident that there is an urgent need to significantly reduce the sensing cost (i.e., the number of expensive sensors) as well as the related memory and bandwidth requirements by developing unconventional sensing mechanisms to extract as much information as possible yet collecting fewer data. The aim of this monograph is therefore to develop theory and algorithms for smart data reduction. We develop a data reduction tool called sparse sensing, which consists of a deterministic and structured sensing function (guided by a sparse vector) that is optimally designed to achieve a desired inference performance with the reduced number of data samples. We develop sparse sensing mechanisms, convex programs, and greedy algorithms to efficiently design sparse sensing functions, where we assume that the data is not yet available and the model information is perfectly known. Sparse sensing offers a number of advantages over compressed sensing (a state-of-the-art data reduction method for sparse signal recovery). One of the major differences is that in sparse sensing the underlying signals need not be sparse. This allows for general signal processing tasks (not just sparse signal recovery) under the proposed sparse sensing framework. Specifically, we focus on fundamental statistical inference tasks, like estimation, filtering, and detection. In essence, we present topics that transform classical (e.g., random or uniform) sensing methods to low-cost data acquisition mechanisms tailored for specific inference tasks. The developed framework can be applied to sensor selection, sensor placement, or sensor scheduling, for example. S.P. Chepuri and G. Leus. Sparse Sensing for Statistical Inference. Foundations and Trends R © in Signal Processing, vol. 9, no. 3-4, pp. 233–386, 2015. DOI: 10.1561/2000000069. Full text available at: http://dx.doi.org/10.1561/2000000069