From Sparse Signals to Sparse Residuals for Robust Sensing

Recent advances in sensor technology have made it feasible to deploy a network of inexpensive sensors for carrying out synergistically even sophisticated inference tasks. In applications such as environmental monitoring, surveillance of critical infrastructure, agriculture, or medical imaging, the typical concept of operation involves a large and possibly heterogeneous set of sensors locally observing the signal of interest, and transmitting their measurements to a higher-layer agent (fusion center). This so-termed layered sensing apparatus entails three operational conditions: (c1) Each node's measurement vector comprising either a collection of scalar observations across time, or a snapshot of different sensor readings, is typically assumed to be linearly related to the unknown variable(s). Such a linear model can arise when the sensing system is viewed as a linear filter with known impulse response. Even when the underlying model is nonlinear, the observations are approximately modeled as adhering to a (multivariate) linear regression; (c2) Either because readings are costly to sense and transmit, due to delay or stationarity constraints, or simply because dimensionality reduction is invoked to cope with the "curse of dimensionality," the linear model is oftentimes under-determined, i.e., the dimension of the unknown vector is larger than that of each sensor's vector observation; and (c3) Not all sensors are reliable because failures in the sensing devices, fades of the sensor-agent communication link, physical obstruction of the scene of interest, and (un)intentional interference, all can severely deteriorate the consistency and reliability of sensor data.