Distributed Field Reconstruction in Sensor Networks |
||
|
||
|
DESCRIPTION/ABSTRACT: High resolution remote sensing of physical phenomena is a task of considerable importance in applications such as environment monitoring, ecology, and precision agriculture. A central unit, having access to the data acquired by a dense distributed network of low-precision, noisy, unreliable, low-power sensors, operating under stringent inter-sensor communication constraints, is required to reconstruct the spatio-temporal field to maximum accuracy. The goal is to efficiently acquire, process, and transport data to faithfully reconstruct the field under appropriate measures of fidelity. Following a quick introduction, overview, and perspective of the research area, the first part of this short-course re-examines the classical problem of sampling a spatially bandlimited field using fixed precision sensors but under distributed processing and communication constraints. An underlying "conservation of bits" principle is exposed: the bit-budget per Nyquist-interval per snapshot (the rate) can be flexibly traded off between the sensor density (spatial axis) and the sensor precision (amplitude axis) in an almost arbitrary discrete-valued manner, while retaining the best-known (exponential) distortion-rate characteristics. With only neighbor-to-neighbor communication, distributed coding, and appropriate interpolation algorithms, an achievable "information scaling law" for field reconstruction over a bounded region is also derived. Both deterministic and stochastic field models are discussed. For stochastic fields, results are established in the almost-sure sense. The focus of the second part of the course shifts to the extremes of lack of control in the sensor deployment, arbitrariness and lack of complete knowledge of the sensing noise distribution, and low-precision and unreliability in the sensors. A constructive quantization, coding, and field reconstruction scheme is developed and an upper-bound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatio-temporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain weak technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the per-sensor bitrate and sensing-related network overhead rate simultaneously go to zero. Almost sure and mean-square convergence of the proposed estimator to the field as the number of sensors tends to infinity is also established. The estimator achieves the best possible rate of decay of MSE with increasing sensor density for both finite-dimensional and Sobolev differentiable fields. SPEAKER BIO: Prakash Ishwar received the BTech degree in EE from IIT Bombay, India, in 1996 and the MS and PhD degrees in ECE from UIUC in 1998 and 2002 respectively. After a 2-year post-doctoral stint in the EECS Department at UC Berkeley he joined Boston University where he is currently an Assistant Professor in the ECE Department and a faculty member in the Information Systems and Sciences group, the Center for Information and Systems Engineering, and the Sensor Network Consortium. He was awarded the 2000 Mavis College of Engineering Fellowship of UIUC and he received the US NSF CAREER award in Dec'05. His research interests lie at the intersection of signal processing, communications, and information theory. Web page: http://iss.bu.edu/pi |
