Weighted l-1 Minimization for Event Detection in Sensor Networks

Event detection is an important application of wireless sensor networks. When the event signature is sparse in a known domain, mechanisms from the emerging area of Compressed Sensing (CS) can be applied for estimation with average measurement rates far lower than the Nyquist requirement. A recently proposed algorithm called IDEA uses knowledge of where the signal is sparse combined with a greedy search procedure called Orthogonal Matching Pursuit (OMP) to demonstrate that detection can be performed in the sparse domain with even fewer measurements. A different approach called Basis Pursuit (BP), which uses l-1 norm minimization, provides better performance in reconstruction but suffers from a larger sampling cost since it tries to estimate the signal completely. In this paper, we introduce a mechanism that uses a modified BP approach for detection of sparse signals with known signature. The modification is inspired from a novel development that uses an adaptively weighted version of BP. We show, through simulation and experiments on MicaZ motes, that by appropriately weighting the coefficients during l-1 norm minimization, detection performance exceeds that of an unweighted approach at comparable sampling rates. Sponsored in part by the U.S. Office of Naval Research under MURI-VA Tech Award CR-19097-430345. The original document contains color images. All DTIC reproductions will be in black and white.