Distributed field reconstruction with model-robust basis pursuit

We study the use of distributed average consensus and compressed sensing to perform decentralized estimation of a field measured by networked sensors. We examine field reconstruction of multiple acoustic sources from isotropic magnitude measurements. Compressed projections of global network observations are spread throughout the network using consensus, after which all nodes may invert the source field using ℓ₁ recovery methods. To approximate the problem as a discrete linear system, the space of source locations is quantized, introducing model error. We propose a model-robust adaptation to basis pursuit to control for the error arising from the spatial quantization. We show conditions for stability of the robust estimator, providing bounds on the reconstruction error based on perturbation constants, source magnitudes, and mutual coherence. Experiments show that the two types of robust estimators successfully address infeasibility and consistency issues that arise in basis pursuit for spatially quantized acoustic sources.