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      • Department of Electrical and Electronics Engineering
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      Optimal measurement under cost constraints for estimation of propagating wave fields

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      Author
      Özçelikkale, Ayça
      Özaktaş, Haldun M.
      Arıkan, Erdal
      Date
      2007
      Source Title
      Proceedings of the International Symposium on Information Theory, ISIT 2007
      Print ISSN
      2157-8101
      Publisher
      IEEE
      Pages
      696 - 700
      Language
      English
      Type
      Conference Paper
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      Abstract
      We give a precise mathematical formulation of some measurement problems arising in optics, which is also applicable in a wide variety of other contexts. In essence the measurement problem is an estimation problem in which data collected by a number of noisy measurement probes arc combined to reconstruct an unknown realization of a random process f(x) indexed by a spatial variable x ε ℝk for some k ≥ 1. We wish to optimally choose and position the probes given the statistical characterization of the process f(x) and of the measurement noise processes. We use a model in which we define a cost function for measurement probes depending on their resolving power. The estimation problem is then set up as an optimization problem in which we wish to minimize the mean-square estimation error summed over the entire domain of f subject to a total cost constraint for the probes. The decision variables are the number of probes, their positions and qualities. We are unable to offer a solution to this problem in such generality; however, for the metrical problem in which the number and locations or the probes are fixed, we give complete solutions Tor some special cases and an efficient numerical algorithm for computing the best trade-off between measurement cost and mean-square estimation error. A novel aspect of our formulation is its close connection with information theory; as we argue in the paper, the mutual information function is the natural cost function for a measurement device. The use of information as a cost measure for noisy measurements opens up several direct analogies between the measurement problem and classical problems of information theory, which are pointed out in the paper.
      Keywords
      Wave fields
      Information theory
      Random processes
      Technical presentations
      Permalink
      http://hdl.handle.net/11693/26938
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/ISIT.2007.4557306
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