Weighted l-1 Minimization for Event Detection in Sensor Networks [Report]

NESL Technical Report #: 2009-5-1


Abstract: 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 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 norm minimization, detection performance exceeds that of an unweighted approach at comparable sampling rates.

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Page (Count): 7

Date: 2009-05-03

Public Document?: Yes

NESL Document?: Yes

Document category: Report