Field inversion by consensus and compressed sensing

We study the inversion of a random field from pointwise measurements collected by a sensor network. We assume that the field has a sparse representation in a known basis. To illustrate the approach, consider the inversion of an acoustic field created by the superposition of a discrete number of propagating noisy acoustic sources. Our method combines compressed sensing (sparse reconstruction by lscr₁-constrained optimization) with distributed average consensus (mixing the pointwise sensor measurements by local communication among the sensors). The paper describes the approach and demonstrates its good performance with synthetic data for several scenarios of practical interest.