Distributed Sparse Signal Recovery For Sensor Networks

We propose a distributed algorithm for sparse signal recovery in sensor networks based on Iterative Hard Thresholding (IHT). Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements at a minimal communication cost and with low computational complexity. A naive distributed implementation of IHT would require global communication of every agent's full state in each iteration. We find that we can dramatically reduce this communication cost by leveraging solutions to the distributed top-K problem in the database literature. Evaluations show that our algorithm requires up to three orders of magnitude less total bandwidth than the best-known distributed basis pursuit method

Pushing towards the Limit of Sampling Rate: Adaptive Chasing Sampling

Measurement samples are often taken in various monitoring applications. To reduce the sensing cost, it is desirable to achieve better sensing quality while using fewer samples. Compressive Sensing (CS) technique finds its role when the signal to be sampled meets certain sparsity requirements. In this paper we investigate the possibility and basic techniques that could further reduce the number of samples involved in conventional CS theory by exploiting learning-based non-uniform adaptive sampling. Based on a typical signal sensing application, we illustrate and evaluate the performance of two of our algorithms, Individual Chasing and Centroid Chasing, for signals of different distribution features. Our proposed learning-based adaptive sampling schemes complement existing efforts in CS fields and do not depend on any specific signal reconstruction technique. Compared to conventional sparse sampling methods, the simulation results demonstrate that our algorithms allow $46\%$ less number of samples for accurate signal reconstruction and achieve up to $57\%$ smaller signal reconstruction error under the same noise condition.Comment: 9 pages, IEEE MASS 201

Distributed Basis Pursuit

We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes. The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix A at any time. We consider two scenarios in which either the columns or the rows of A are distributed among the compute nodes. Our algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multipliers. We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms.Comment: Preprint of the journal version of the paper; IEEE Transactions on Signal Processing, Vol. 60, Issue 4, April, 201

Sparse Localization with a Mobile Beacon Based on LU Decomposition in Wireless Sensor Networks

Node localization is the core in wireless sensor network. It can be solved by powerful beacons, which are equipped with global positioning system devices to know their location information. In this article, we present a novel sparse localization approach with a mobile beacon based on LU decomposition. Our scheme firstly translates node localization problem into a 1-sparse vector recovery problem by establishing sparse localization model. Then, LU decomposition pre-processing is adopted to solve the problem that measurement matrix does not meet the re¬stricted isometry property. Later, the 1-sparse vector can be exactly recovered by compressive sensing. Finally, as the 1-sparse vector is approximate sparse, weighted Cen¬troid scheme is introduced to accurately locate the node. Simulation and analysis show that our scheme has better localization performance and lower requirement for the mobile beacon than MAP+GC, MAP-M, and MAP-M&N schemes. In addition, the obstacles and DOI have little effect on the novel scheme, and it has great localization performance under low SNR, thus, the scheme proposed is robust