Browsing by Subject "Random field estimation"

Now showing 1 - 4 of 4

Open Access
Choice of sampling interval and extent for finite-energy fields
(Institute of Electrical and Electronics Engineers Inc., 2017) Gulcu, T. C.; Özaktaş, Haldun M.
We focus on the problem of representing a nonstationary finite-energy random field, with finitely many samples. We do not require the field to be of finite extent or to be bandlimited. We propose an optimizable procedure for obtaining a finite-sample representation of the given field. We estimate the reconstruction error of the procedure, showing that it is the sum of the truncation errors in the space and frequency domains. We also optimize the truncation parameters analytically and present the resultant Pareto-optimal tradeoff curves involving the error in reconstruction and the sample count, for several examples. These tradeoff curves can be used to determine the optimal sampling strategy in a practical situation based on the relative importance of error and sample count for that application.
Open Access
Optimal representation of non-stationary random fields with finite numbers of samples: A linear MMSE framework
(Elsevier, 2013) Özçelikkale, A.; Özaktaş, Haldun M.
In this article we consider the representation of a finite-energy non-stationary random field with a finite number of samples. We pose the problem as an optimal sampling problem where we seek the optimal sampling interval under the mean-square error criterion, for a given number of samples. We investigate the optimum sampling rates and the resulting trade-offs between the number of samples and the representation error. In our numerical experiments, we consider a parametric non-stationary field model, the Gaussian-Schell model, and present sampling schemes for varying noise levels and for sources with varying numbers of degrees of freedom. We discuss the dependence of the optimum sampling interval on the problem parameters. We also study the sensitivity of the error to the chosen sampling interval.
Open Access
Signal recovery with cost-constrained measurements
(IEE, 2010-03-22) Özçelikkale, A.; Özaktaş, Haldun M.; Arikan, E.
We are concerned with the problem of optimally measuring an accessible signal under a total cost constraint, in order to estimate a signal which is not directly accessible. An important aspect of our formulation is the inclusion of a measurement device model where each device has a cost depending on the number of amplitude levels that the device can reliably distinguish. We also assume that there is a cost budget so that it is not possible to make a high amplitude resolution measurement at every point. We investigate the optimal allocation of cost budget to the measurement devices so as to minimize estimation error. This problem differs from standard estimation problems in that we are allowed to design the number and noise levels of the measurement devices subject to the cost constraint. Our main results are presented in the form of tradeoff curves between the estimation error and the cost budget. Although our primary motivation and numerical examples come from wave propagation problems, our formulation is also valid for other measurement problems with similar budget limitations where the observed variables are related to the unknown variables through a linear relation. We discuss the effects of signal-to-noise ratio, distance of propagation, and the degree of coherence (correlation) of the waves on these tradeoffs and the optimum cost allocation. Our conclusions not only yield practical strategies for designing optimal measurement systems under cost constraints, but also provide insights into measurement aspects of certain inverse problems.
Open Access
Unitary precoding and basis dependency of MMSE performance for gaussian erasure channels
(IEEE, 2014) Özçelikkale, A.; Yüksel S.; Özaktaş, Haldun M.
We consider the transmission of a Gaussian vector source over a multidimensional Gaussian channel where a random or a fixed subset of the channel outputs are erased. Within the setup where the only encoding operation allowed is a linear unitary transformation on the source, we investigate the minimum mean-square error (MMSE) performance, both in average, and also in terms of guarantees that hold with high probability as a function of the system parameters. Under the performance criterion of average MMSE, necessary conditions that should be satisfied by the optimal unitary encoders are established and explicit solutions for a class of settings are presented. For random sampling of signals that have a low number of degrees of freedom, we present MMSE bounds that hold with high probability. Our results illustrate how the spread of the eigenvalue distribution and the unitary transformation contribute to these performance guarantees. The performance of the discrete Fourier transform (DFT) is also investigated. As a benchmark, we investigate the equidistant sampling of circularly wide-sense stationary signals, and present the explicit error expression that quantifies the effects of the sampling rate and the eigenvalue distribution of the covariance matrix of the signal. These findings may be useful in understanding the geometric dependence of signal uncertainty in a stochastic process. In particular, unlike information theoretic measures such as entropy, we highlight the basis dependence of uncertainty in a signal with another perspective. The unitary encoding space restriction exhibits the most and least favorable signal bases for estimation. © 2014 IEEE.