Distributed sensing of noisy signals by thresholding of redundant expansions

This paper addresses the problem of sensing or recovering a signal s, captured by distributed low-complexity sensors. Each sensor observes a noisy version of the signal of interest, and independently forms an approximant of its observation. This approximant is sent to a central decoder that tries to recover the input signal by combining the multiple sensor outputs. We propose to use redundant dictionaries, and thresholding in the sensor nodes, in order to form sparse approximants of the noisy observations, with low computational complexity. We first show that the noise can actually be beneficial in the recovery of the correct components of the signal s, since it can advantageously perturb the naive thresholding scheme. Then we illustrate the benefit of multiple observations with uncorrelated noise. By careful reconstruction with a POCS strategy, each additional measurement actually helps to recover more and more components of the original signal, since it tends to isolate the common part in all observations. Experimental results demonstrate the interesting recovery performance of our distributed sensing system. They show that a few observations, represented by a small number of components, are able to provide a good approximation of the signal, even in very noisy conditions.