Browsing by Subject "Average errors"

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Open Access
Average error in recovery of sparse signals and discrete fourier transform
(IEEE, 2012-04) Özçelikkale, Ayça; Yüksel, S.; Özaktaş Haldun M.
In compressive sensing framework it has been shown that a sparse signal can be successfully recovered from a few random measurements. The Discrete Fourier Transform (DFT) is one of the transforms that provide the best performance guarantees regardless of which components of the signal are nonzero. This result is based on the performance criterion of signal recovery with high probability. Whether the DFT is the optimum transform under average error criterion, instead of high probability criterion, has not been investigated. Here we consider this optimization problem. For this purpose, we model the signal as a random process, and propose a model where the covariance matrix of the signal is used as a measure of sparsity. We show that the DFT is, in general, not optimal despite numerous results that suggest otherwise. © 2012 IEEE.
Open Access
Synthetic TEC mapping with kriging and random field priors
(IEEE, 2007) Sayın, I.; Arıkan, F.; Arıkan, Orhan
Total Electron Content (TEC) can be used for analyzing the variability of the ionosphere in space and time. In this study, spatial interpolation is implemented by Kriging and Random Field Priors (RFP), which are widely used in geostatistics. Performance of Kriging and RFP methods are analyzed on synthetic TEC data for different trend functions, sampling patterns, sampling numbers, variance and range values of covariance function which is used to simulate the synthetic data, by comparing the normalized errors of interpolations. In regular sampling patterns, as opposed to random sampling, the normalized average error is very close to each other for all methods and trend assumptions. The error increases with variance and decreases with range. As the number of samples increase, the normalized error also decreases.