Browsing by Subject "Gaussians"
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Item Open Access Average Fisher information maximisation in presence of cost-constrained measurements(The Institution of Engineering and Technology, 2011) Dulek, B.; Gezici, SinanAn optimal estimation framework is considered in the presence of cost-constrained measurements. The aim is to maximise the average Fisher information under a constraint on the total cost of measurement devices. An optimisation problem is formulated to calculate the optimal costs of measurement devices that maximise the average Fisher information for arbitrary observation and measurement statistics. In addition, a closed-form expression is obtained in the case of Gaussian observations and measurement noise. Numerical examples are presented to explain the results.Item Open Access Entropy minimization based robust algorithm for adaptive networks(IEEE, 2012) Köse, Kıvanç; Çetin, A. Enis; Gunay O.In this paper, the problem of estimating the impulse responses of individual nodes in a network of nodes is dealt. It was shown by the previous work in literature that when the nodes can interact with each other, fusion based adaptive filtering approaches are more effective than handling nodes independently. Here we are proposing the use of entropy functional based optimization in the adaptive filtering stage. We tested the new method on networks under Gaussian and ε-contaminated Gaussian noise. The results show that the proposed method achieves significant improvements in the error rates in case of ε-contaminated noise. © 2012 IEEE.Item Open Access Fast and accurate algorithm for the computation of complex linear canonical transforms(Optical Society of America, 2010-08-05) Koç A.; Özaktaş, Haldun M.; Hesselink, L.A fast and accurate algorithm is developed for the numerical computation of the family of complex linear canonical transforms (CLCTs), which represent the input-output relationship of complex quadratic-phase systems. Allowing the linear canonical transform parameters to be complex numbers makes it possible to represent paraxial optical systems that involve complex parameters. These include lossy systems such as Gaussian apertures, Gaussian ducts, or complex graded-index media, as well as lossless thin lenses and sections of free space and any arbitrary combinations of them. Complex-ordered fractional Fourier transforms (CFRTs) are a special case of CLCTs, and therefore a fast and accurate algorithm to compute CFRTs is included as a special case of the presented algorithm. The algorithm is based on decomposition of an arbitrary CLCT matrix into real and complex chirp multiplications and Fourier transforms. The samples of the output are obtained from the samples of the input in ∼N log N time, where N is the number of input samples. A space-bandwidth product tracking formalism is developed to ensure that the number of samples is information-theoretically sufficient to reconstruct the continuous transform, but not unnecessarily redundant.Item Open Access Gauss tabanlı modelleme kullanarak canlı hücre görüntülerinin öğreticisiz bölütlenmesi(2011-04) Arslan, Salim; Durmaz, İrem; Çetin-Atalay, Rengül; Gündüz-Demir, ÇiğdemThe first step of targeted cancer drug development is to screen and determine drug candidates by in vitro measuring the effectiveness of the drugs. The tests developed for this purpose can be time consuming due to their procedures and cannot be conducted in every laboratory due to the required hardwares. On the other hand, an image-based screening test has a potential to be less time consuming since it can directly be carried out on the live cell images and to be more extensively used because of the availability of its required equipments and their relatively less expensive cost. With such an image-based test, it is possible to quantify the cell death by finding cellular regions and comparing it against the control group. In this work, we propose a new method that automatically locates the cellular regions by the unsupervised segmentation of live cell images. This method relies on approximately locating cellular regions and the background with gradient-based thresholding and morphological operators and then finding the final boundaries by modeling the gradient of these regions with Gaussians. Working on the images of different cell lines captured with different magnifications, our experiments show that the proposed method leads to promising results. © 2011 IEEE.Item Open Access Parameter estimation for synthetic TEC surfaces by using Particle Swarm Optimization(IEEE, 2012) Gökdaǧ, Y.E.; Arikan F.; Toker, C.; Arıkan, OrhanIn this study, parameter estimation is made for global ionospheric Total Electron Content (TEC) on both noiseless and noisy synthetic surfaces by using modified Particle Swarm Optimization (PSO). In addition, the improvements made in the PSO algorithm to obtain better results are presented. Trend functions that best regionally and globally represent the quiet and distorted ionosphere are given. For noisy trend surfaces, additive white Gaussian noise is added on trend surfaces according to latitude. International GPS System stations (IGS) are used for regional sampling whereas TNPGN-Active stations are used for both regional and global sampling. A brief discussion of PSO and its improvements for modified PSO is provided. Performance and error criterias are determined for the results of noisy and noiseless dual-core Gaussian trend surfaces. © 2012 IEEE.Item Open Access Performance analysis of scalar diffusion strategy over distributed network(IEEE, 2014) Sayın, Muhammed Ö.; Kozat, Süleyman SerdarIn this paper, we present a complete performance analysis of the scalar diffusion strategies over distributed networks. Scalar diffusion strategies are based on the diffusion implementation and adaptive extraction of the information from the diffusion data which is compressed into a scalar. This strategy require significantly less communication load while achieving similar performance with the full information exchange configuration. Here, we provide the transient and steady-state analysis of the scalar diffusion strategies for Gaussian regressors. Finally, in the numerical examples, we demonstrate that the theoretical results match with the simulation results.Item Open Access Sıkıştırılmış algılama kullanarak yeni bir yüz gösterimi(IEEE, 2011-04) Eleyan, A.; Köse, Kıvanç; Çetin, A. EnisBu bildiride yüz resimleri için yeni bir tanımlayıcı sunulmaktadır. Sıkıştırılmış Algılama (Compressive Sensing) fikri kullanılarak, yüz imgelerinden öznitelikler çıkarılmıştır. Öznitelik çıkarımı sırasında Rastgele Gauss dağılımına sahip elemanları ya da rasgele ikili elemanları olan ölçüm matrisleri kullanılmıştır. Bu sayede elde edilen öznitelik vektörleri en yakın komşu sınıflandırıcısı kullanılarak sınıflandırılmıştır. Hesaplama karmaşıklığı konusunda büyük bir indirim sağlanmış ve bunun yanında tanıma oranlarında büyük bir düşüş yaşanmamıştır.Item Open Access Time-frequency analysis of signals using support adaptive Hermite-Gaussian expansions(Elsevier, 2012-05-18) Alp, Y. K.; Arıkan, OrhanSince Hermite-Gaussian (HG) functions provide an orthonormal basis with the most compact time-frequency supports (TFSs), they are ideally suited for time-frequency component analysis of finite energy signals. For a signal component whose TFS tightly fits into a circular region around the origin, HG function expansion provides optimal representation by using the fewest number of basis functions. However, for signal components whose TFS has a non-circular shape away from the origin, straight forward expansions require excessively large number of HGs resulting to noise fitting. Furthermore, for closely spaced signal components with non-circular TFSs, direct application of HG expansion cannot provide reliable estimates to the individual signal components. To alleviate these problems, by using expectation maximization (EM) iterations, we propose a fully automated pre-processing technique which identifies and transforms TFSs of individual signal components to circular regions centered around the origin so that reliable signal estimates for the signal components can be obtained. The HG expansion order for each signal component is determined by using a robust estimation technique. Then, the estimated components are post-processed to transform their TFSs back to their original positions. The proposed technique can be used to analyze signals with overlapping components as long as the overlapped supports of the components have an area smaller than the effective support of a Gaussian atom which has the smallest time-bandwidth product. It is shown that if the area of the overlap region is larger than this threshold, the components cannot be uniquely identified. Obtained results on the synthetic and real signals demonstrate the effectiveness for the proposed time-frequency analysis technique under severe noise cases.Item 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.