Spatio-Temporal Sampling of Physical Fields by a Network of Sensors

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• Dr Yue Lu - Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland
• Monday 03 August 2009, 14:00-15:00
• Room 610 - Gabor room.

If you have a question about this talk, please contact Pier Luigi Dragotti.

Sampling, or the conversion of continuous-domain analog signals to discrete numbers suitable for computer processing, is one of the cornerstones of our digital revolution. This talk presents recent work on the topic of distributed spatio-temporal sampling of physical fields by a network of sensors.

The basic questions are simple: Suppose we observe a field governed by a PDE and driven by an unknown source distribution. To perfectly reconstruct the field, or to reliably estimate the source, how many sensors do we need, where should we place them in space, and how often should each sensor take samples over time? The theoretical understanding of the fundamental limits and tradeoff, as well as algorithmic developments of the above sampling problem have implications in many scientific and engineering disciplines. Some examples are pollution monitoring, spatial audio recording, geophysical explorations, and spatial radar applications, to name a few.

In this talk, I will describe the unique challenges faced in the above sampling problem, as well as its connections with the classical multidimensional Shannon sampling theory and the more recent compressed sensing framework. I will then present my work on two concrete problems.

First, I will discuss the sampling and reconstruction of diffusion fields (e.g. temperature variations, pollution distributions). I will show that, by exploiting the spatio-temporal correlation offered by the diffusion PDE , it is possible to achieve a rigorous trade-off between the required spatial and temporal sampling densities. Specifically, by oversampling in time, we can significantly improve the spatial resolution of the reconstructed field, even though the spatial density of the sensors is sub-Nyquist, thus allowing super-resolution in space.

Next, I will focus on wave fields (e.g. the sound pressure field in an auditorium) induced by spatially-localized sources. By exploiting the sparsity of the Green’s functions, I will show how to develop a distributed sampling framework, akin to the Slepian-Wolf setup in source coding, which can dramatically reduce the sampling rates required at distributed sensors.

Finally, I will outline a few more results and topics of current research, indicating how the framework can be used across many applications of signal processing and communications.

This talk is part of the Pier Luigi Dragotti's list series.

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