Distributed Compressed Sensing for Sensor Networks with Packet Erasures

We study two approaches to distributed compressed sensing for in-network data compression and signal reconstruction at a sink in a wireless sensor network where sensors are placed on a straight line. Communication to the sink is considered to be bandwidth-constrained due to the large number of devices. By using distributed compressed sensing for compression of the data in the network, the communication cost (bandwith usage) to the sink can be decreased at the expense of delay induced by the local communication necessary for compression. We investigate the relation between cost and delay given a certain reconstruction performance requirement when using basis pursuit denoising for reconstruction. Moreover, we analyze and compare the performance degradation due to erased packets sent to the sink of the two approaches.Comment: Paper accepted to GLOBECOM 201

An Overview of Multi-Processor Approximate Message Passing

Approximate message passing (AMP) is an algorithmic framework for solving linear inverse problems from noisy measurements, with exciting applications such as reconstructing images, audio, hyper spectral images, and various other signals, including those acquired in compressive signal acquisiton systems. The growing prevalence of big data systems has increased interest in large-scale problems, which may involve huge measurement matrices that are unsuitable for conventional computing systems. To address the challenge of large-scale processing, multiprocessor (MP) versions of AMP have been developed. We provide an overview of two such MP-AMP variants. In row-MP-AMP, each computing node stores a subset of the rows of the matrix and processes corresponding measurements. In column- MP-AMP, each node stores a subset of columns, and is solely responsible for reconstructing a portion of the signal. We will discuss pros and cons of both approaches, summarize recent research results for each, and explain when each one may be a viable approach. Aspects that are highlighted include some recent results on state evolution for both MP-AMP algorithms, and the use of data compression to reduce communication in the MP network

Low-power distributed sparse recovery testbed on wireless sensor networks

Recently, distributed algorithms have been proposed for the recovery of sparse signals in networked systems, e.g. wire- less sensor networks. Such algorithms allow large networks to operate autonomously without the need of a fusion center, and are very appealing for smart sensing problems employing low-power devices. They exploit local communications, where each node of the network updates its estimates of the sensed signal also based on the correlated information received from neighboring nodes. In the literature, theoretical results and numerical simulations have been presented to prove convergence of such methods to accurate estimates. Their implementation, however, raises some concerns in terms of power consumption due to iterative inter- node communications, data storage, computation capabilities, global synchronization, and faulty communications. On the other hand, despite these potential issues, practical implementations on real sensor networks have not been demonstrated yet. In this paper we fill this gap and describe a successful implementation of a class of randomized, distributed algorithms on a real low-power wireless sensor network testbed with very scarce computational capabilities. We consider a distributed compressed sensing problem and we show how to cope with the issues mentioned above. Our tests on synthetic and real signals show that distributed compressed sensing can successfully operate in a real-world environment

Distributed Quantization for Sparse Time Sequences

Analog signals processed in digital hardware are quantized into a discrete bit-constrained representation. Quantization is typically carried out using analog-to-digital converters (ADCs), operating in a serial scalar manner. In some applications, a set of analog signals are acquired individually and processed jointly. Such setups are referred to as distributed quantization. In this work, we propose a distributed quantization scheme for representing a set of sparse time sequences acquired using conventional scalar ADCs. Our approach utilizes tools from secure group testing theory to exploit the sparse nature of the acquired analog signals, obtaining a compact and accurate representation while operating in a distributed fashion. We then show how our technique can be implemented when the quantized signals are transmitted over a multi-hop communication network providing a low-complexity network policy for routing and signal recovery. Our numerical evaluations demonstrate that the proposed scheme notably outperforms conventional methods based on the combination of quantization and compressed sensing tools