23 January 2014
I am going to talk about some recent---and not yet complete--theoretical developments of our work (me, Amina and Martin) on sensor placement in inverse problems. The presentation contains also some practical results, in two directions:
- a joint work with Runwei and Zichong on sensor scheduling in environmental WSN.
- a joint work with Alessandro Vincenzi and David Atienza on sensor placement in many-core processors.
Here is a not-so-short abstract.
Near-Optimal Sensor Placement for Linear Inverse Problems
In many human activities, it is of interest to measure physical phenomena that varies in space and time. Modern approaches tackling this problem are often based on wireless sensor networks (WSN), that are systems composed by many sensing nodes, each capable of measuring, storing, processing and communicating information of the surrounding environment. The design of a WSN is cluttered by challenges and trade-offs and it is a science in itself. One of the key aspects to design a successful WSN is the optimization of the spatial locations of the sensors nodes, given its impact on many relevant indicators, such as coverage, energy consumption and connectivity. When the data collected by the WSN is used to solve inverse problems the importance of sensor locations is even more critical. In fact, the sensor locations determine the error in the solution of the inverse problem and its optimization represents the difference between being able or not being able to obtain a reasonable solution.
The sensor placement problem is combinatorial in itself. In this work, we present a greedy algorithm, called SmartSense. It is the only known algorithm that is near-optimal w.r.t. mean square error and has polynomial complexity. We analyze its theoretical performance using tools from frame theory and submodular optimization. An analysis of its performance compared to the state-of-the-art on both synthetic and real-world data is also proposed. In particular, we will show you results regarding sensor scheduling in environmental WSN and sensor placement in many-core processors.
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