Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

Eigenvector Synchronization, Graph Rigidity and the Molecule Problem

The graph realization problem has received a great deal of attention in recent years, due to its importance in applications such as wireless sensor networks and structural biology. In this paper, we extend on previous work and propose the 3D-ASAP algorithm, for the graph realization problem in $\mathbb{R}^3$, given a sparse and noisy set of distance measurements. 3D-ASAP is a divide and conquer, non-incremental and non-iterative algorithm, which integrates local distance information into a global structure determination. Our approach starts with identifying, for every node, a subgraph of its 1-hop neighborhood graph, which can be accurately embedded in its own coordinate system. In the noise-free case, the computed coordinates of the sensors in each patch must agree with their global positioning up to some unknown rigid motion, that is, up to translation, rotation and possibly reflection. In other words, to every patch there corresponds an element of the Euclidean group Euc(3) of rigid transformations in $\mathbb{R}^3$, and the goal is to estimate the group elements that will properly align all the patches in a globally consistent way. Furthermore, 3D-ASAP successfully incorporates information specific to the molecule problem in structural biology, in particular information on known substructures and their orientation. In addition, we also propose 3D-SP-ASAP, a faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a preprocessing step for dividing the initial graph into smaller subgraphs. Our extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very robust to high levels of noise in the measured distances and to sparse connectivity in the measurement graph, and compare favorably to similar state-of-the art localization algorithms.Comment: 49 pages, 8 figure

Lifetime Maximization of an Internet of Things (IoT) Network based on Graph Signal Processing

The lifetime of an Internet of Things (IoT) system consisting of battery-powered devices can be increased by minimizing the number of transmissions per device while not excessively deteriorating the correctness of the overall IoT monitoring. We propose a graph signal processing based algorithm for partitioning the sensor nodes into disjoint sampling sets. The sets can be sampled on a round-robin basis and each one contains enough information to reconstruct the entire signal within an acceptable error bound. Simulations on different models of graphs, based on graph theory and on real-world applications, show that our proposal consistently outperforms state-of-the-art sampling schemes, with no additional computational burden

On a registration-based approach to sensor network localization

We consider a registration-based approach for localizing sensor networks from range measurements. This is based on the assumption that one can find overlapping cliques spanning the network. That is, for each sensor, one can identify geometric neighbors for which all inter-sensor ranges are known. Such cliques can be efficiently localized using multidimensional scaling. However, since each clique is localized in some local coordinate system, we are required to register them in a global coordinate system. In other words, our approach is based on transforming the localization problem into a problem of registration. In this context, the main contributions are as follows. First, we describe an efficient method for partitioning the network into overlapping cliques. Second, we study the problem of registering the localized cliques, and formulate a necessary rigidity condition for uniquely recovering the global sensor coordinates. In particular, we present a method for efficiently testing rigidity, and a proposal for augmenting the partitioned network to enforce rigidity. A recently proposed semidefinite relaxation of global registration is used for registering the cliques. We present simulation results on random and structured sensor networks to demonstrate that the proposed method compares favourably with state-of-the-art methods in terms of run-time, accuracy, and scalability

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

Iterative Slepian-Wolf Decoding and FEC Decoding for Compress-and-Forward Systems

While many studies have concentrated on providing theoretical analysis for the relay assisted compress-and-forward systems little effort has yet been made to the construction and evaluation of a practical system. In this paper a practical CF system incorporating an error-resilient multilevel Slepian-Wolf decoder is introduced and a novel iterative processing structure which allows information exchanging between the Slepian-Wolf decoder and the forward error correction decoder of the main source message is proposed. In addition, a new quantization scheme is incorporated as well to avoid the complexity of the reconstruction of the relay signal at the final decoder of the destination. The results demonstrate that the iterative structure not only reduces the decoding loss of the Slepian-Wolf decoder, it also improves the decoding performance of the main message from the source

Data Compression in Multi-Hop Large-Scale Wireless Sensor Networks

Data collection from a multi-hop large-scale outdoor WSN deployment for environmental monitoring is full of challenges due to the severe resource constraints on small battery-operated motes (e.g., bandwidth, memory, power, and computing capacity) and the highly dynamic wireless link conditions in an outdoor communication environment. We present a compressed sensing approach which can recover the sensing data at the sink with good accuracy when very few packets are collected, thus leading to a significant reduction of the network traffic and an extension of the WSN lifetime. Interplaying with the dynamic WSN routing topology, the proposed approach is efficient and simple to implement on the resource-constrained motes without motes storing of a part of random measurement matrix, as opposed to other existing compressed sensing based schemes. We provide a systematic method via machine learning to find a suitable representation basis, for the given WSN deployment and data field, which is both sparse and incoherent with the measurement matrix in the compressed sensing. We validate our approach and evaluate its performance using our real-world multi-hop WSN testbed deployment in situ in collecting the humidity and soil moisture data. The results show that our approach significantly outperforms three other compressed sensing based algorithms regarding the data recovery accuracy for the entire WSN observation field under drastically reduced communication costs. For some WSN scenarios, compressed sensing may not be applicable. Therefore we also design a generalized predictive coding framework for unified lossless and lossy data compression. In addition, we devise a novel algorithm for lossless compression to significantly improve data compression performance for variouSs data collections and applications in WSNs. Rigorous simulations show our proposed framework and compression algorithm outperform several recent popular compression algorithms for wireless sensor networks such as LEC, S-LZW and LTC using various real-world sensor data sets, demonstrating the merit of the proposed framework for unified temporal lossless and lossy data compression in WSNs