Browsing by Author "Dülek, Berkan"

Now showing 1 - 9 of 9

Open Access
A confidence ellipsoid approach for measurement cost minimization under Gaussian noise
(IEEE, 2012-06) Dülek, Berkan; Gezici, Sinan
The well-known problem of estimating an unknown deterministic parameter vector over a linear system subject to additive Gaussian noise is studied from the perspective of minimizing total sensor measurement cost under a constraint on the log volume of the estimation error confidence ellipsoid. A convex optimization problem is formulated for the general case, and a closed form solution is provided when the system matrix is invertible. Furthermore, effects of system matrix uncertainty are discussed by employing a specific but nevertheless practical uncertainty model. Numerical examples are presented to discuss the theoretical results in detail.
Open Access
Convexity properties of outage probability under Rayleigh fading
(IEEE, 2012) Dülek, Berkan; Vanlı, N. Denizcan; Gezici, Sinan
In this paper, convexity properties of outage probability are investigated under Rayleigh fading for an average power-constrained communications system that employs maximal-ratio combining (MRC) at the receiver. By studying the first and second order derivatives of the outage probability with respect to the transmitted signal power, it is found out that the outage probability is a monotonically decreasing function with a single inflection point. This observation suggests the possibility of improving the outage performance via on-off type power randomization/sharing under stringent average transmit power constraints. It is shown that the results can also be extended to the selection combining (SC) technique in a straightforward manner. Finally, a numerical example is provided to illustrate the theoretical results. © 2012 IEEE.
Open Access
Detection of empty hazelnuts from fully developed nuts by impact acoustics
(IEEE, 2005) Onaran, İbrahim; Dülek, Berkan; Pearson, T. C.; Yardımcı, Y.; Çetin, A. Enis
Shell-kernel weight ratio is the main determinate of quality and price of hazelnuts. Empty hazelnuts and nuts containing undeveloped kernels may also contain mycotoxin producing molds, which can cause cancer. A prototype system was set up to detect empty hazelnuts by dropping them onto a steel plate and processing the acoustic signal generated when kernels impact the plate. The acoustic signal was processed by five different methods: 1) modeling of the signal in the time domain, 2) computing time domain signal variances in short time windows, 3) analysis of the frequency spectra magnitudes, 4) maximum amplitude values in short time windows, and 5) line spectral frequencies (LSFs). Support Vector Machines (SVMs) were used to select a subset of features and perform classification. 98% of fully developed kernels and 97% of empty kernels were correctly classified.
Open Access
Human face detection in video using edge projections
(SPIE, 2006) Türkan, Mehmet; Dülek, Berkan; Onaran, İbrahim; Çetin, A. Enis
In this paper, a human face detection method in images and video is presented. After determining possible face candidate regions using color information, each region is filtered by a high-pass filter of a wavelet transform. In this way, edges of the region are highlighted, and a caricature-like representation of candidate regions is obtained. Horizontal, vertical and filter-like projections of the region are used as feature signals in dynamic programming (DP) and support vector machine (SVM) based classifiers. It turns out that the support vector machine based classifier provides better detection rates compared to dynamic programming in our simulation studies.
Open Access
Optimal stochastic approaches for signal detection and estimation under inequality constraints
(2012) Dülek, Berkan
Fundamental to the study of signal detection and estimation is the design of optimal procedures that operate on the noisy observations of some random phenomenon. For detection problems, the aim is to decide among a number of statistical hypotheses, whereas estimating certain parameters of the statistical model is required in estimation problems. In both cases, the solution depends on some goodness criterion by which detection (or estimation) performance is measured. Despite being a well-established field, the advances over the last several decades in hardware and digital signal processing have fostered a renewed interest in designing optimal procedures that take more into account the practical considerations. For example, in the detection of binary-valued scalar signals corrupted with additive noise, an analysis on the convexity properties of the error probability with respect to the transmit signal power has suggested that the error performance cannot be improved via signal power randomization/sharing under an average transmit power constraint when the noise has a unimodal distribution (such as the Gaussian distribution). On the contrary, it is demonstrated that performance enhancement is possible in the case of multimodal noise distributions and even under Gaussian noise for three or higher dimensional signal constellations. Motivated by these results, in this dissertation we adopt a structured approach built on concepts called stochastic signaling and detector randomization, and devise optimal detection procedures for power constrained communications systems operating over channels with arbitrary noise distributions. First, we study the problem of jointly designing the transmitted signals, decision rules, and detector randomization factors for an M-ary communications system with multiple detectors at the receiver. For each detector employed at the receiver, it is assumed that the transmitter can randomize its signal constellation (i.e., transmitter can employ stochastic signaling) according to some probability density function (PDF) under an average transmit power constraint. We show that stochastic signaling without detector randomization cannot achieve a smaller average probability of error than detector randomization with deterministic signaling for the same average power constraint and noise statistics when optimal maximum a-posteriori probability (MAP) detectors are employed in both cases. Next, we prove that a randomization between at most two MAP detectors corresponding to two deterministic signal vectors results in the optimal performance. Sufficient conditions are also provided to conclude ahead of time whether the correct decision performance can or cannot be improved by detector randomization. In the literature, the discussions on the benefits of stochastic signaling and detector randomization are severely limited to the Bayesian criterion. Therefore, we study the convexity/concavity properties for the problem of detecting the presence of a signal emitted from a power constrained transmitter in the presence of additive Gaussian noise under the Neyman-Pearson (NP) framework. First, it is proved that the detection probability corresponding to the α−level likelihood ratio test (LRT) is either concave or has two inflection points such that the function is concave, convex and finally concave with respect to increasing values of the signal power. Based on this result, optimal and near-optimal power sharing/randomization strategies are proposed for average and/or peak power constrained transmitters. Using a similar approach, the convexity/concavity properties of the detection probability are also investigated with respect to the jammer power. The results indicate that a weak Gaussian jammer should employ on-off time sharing to degrade the detection performance. Next, the previous analysis for the NP criterion is generalized to channels with arbitrary noise PDFs. Specifically, we address the problem of jointly designing the signaling scheme and the decision rule so that the detection probability is maximized under constraints on the average false alarm probability and average transmit power. In the case of a single detector at the receiver, it is shown that the optimal solution can be obtained by employing randomization between at most two signal values for the on-signal and using the corresponding NP-type LRT at the receiver. When multiple detectors are available at the receiver, the optimal solution involves a randomization among no more than three NP decision rules corresponding to three deterministic signal vectors. Up to this point, we have focused on signal detection problems. In the following, the trade-offs between parameter estimation accuracy and measurement device cost are investigateed under the influence of noise. First, we seek to determine the most favorable allocation of the total cost to measurement devices so that the average Fisher information of the resulting measurements is maximized for arbitrary observation and measurement statistics. Based on a recently proposed measurement device cost model, we present a generic optimization problem without assuming any specific estimator structure. Closed form expressions are obtained in the case of Gaussian observations and measurement noise. Finally, a more elaborate analysis of the relationship between parameter estimation accuracy and measurement device cost is presented. More specifically, novel convex measurement cost minimization problems are proposed based on various estimation accuracy constraints assuming a linear system subject to additive Gaussian noise for the deterministic parameter estimation problem. Robust allocation of the total cost to measurement devices is also considered by assuming a specific uncertainty model on the system matrix. Closed form solutions are obtained in the case of an invertible system matrix for two estimation accuracy criteria. Through numerical examples, various aspects of the proposed optimization problems are compared. Lastly, the discussion is extended to the Bayesian framework assuming that the estimated parameter is Gaussian distributed.
Open Access
Optimal stochastic signal design and detector randomization in the Neyman-Pearson framework
(IEEE, 2012-03) Dülek, Berkan; Gezici, Sinan
Power constrained on-off keying communications systems are investigated in the presence of stochastic signaling and detector randomization. The joint optimal design of decision rules, stochastic signals, and detector randomization factors is performed. It is shown that the solution to the most generic optimization problem that employs both stochastic signaling and detector randomization can be obtained as the randomization among no more than three Neyman-Pearson (NP) decision rules corresponding to three deterministic signal vectors. Numerical examples are also presented. © 2012 IEEE.
Open Access
Power adaptation for vector parameter estimation according to Fisher information based optimality criteria
(Elsevier BV, 2022-03) Gürgünoğlu, Doğa; Dülek, Berkan; Gezici, Sinan
The optimal power adaptation problem is investigated for vector parameter estimation according to various Fisher information based optimality criteria. By considering an observation model that involves a linear transformation of the parameter vector and an additive noise component with an arbitrary probability distribution, six different optimal power allocation problems are formulated based on Fisher information based objective functions. Via optimization theoretic approaches, various closed-form solutions are derived for the proposed problems. Also, the results are extended to cases in which nuisance parameters exist in the system model or certain types of nonlinear transformations are applied on the parameter vector. Numerical examples are presented to investigate performance of the proposed power allocation strategies.
Open Access
Signal and image processing algorithms for agricultural applications
(2006) Dülek, Berkan
Medical studies indicate that acrylamide causes cancer in animals and certain doses of acrylamide are toxic to the nervous system of both animals and humans. Acrylamide is produced in carbohydrate foods prepared at high temperatures such as fried potatoes. For this reason, it is crucial for human health to quantitatively measure the amount of acrylamide formed as a result of prolonged cooking at high temperatures. In this thesis, a correlation is demonstrated between measured acrylamide concentrations and NABY (Normalized Area of Brownish Yellow regions) values estimated from surface color properties of fried potato images using a modified form of the k-means algorithm. Same method is used to estimate acrylamide levels of roasted coffee beans. The proposed method seems to be a promising approach for the estimation of acrylamide levels and can find applications in industrial systems. The quality and price of hazelnuts are mainly determined by the ratio of shell weight to kernel weight. Due to a number of physiological and physical disorders, hazelnuts may grow without fully developed kernels. We previously proposed a prototype system which detects empty hazelnuts by dropping them onto a steel plate and processing the acoustic signal generated when kernels hit the plate. In that study, feature vectors describing time and frequency nature of the impact sound were extracted from the acoustic signal and classified using Support Vector Machines. In the second part of this thesis, a feature domain post-processing method based on vector median/mean filtering is shown to further increase these classification results.
Open Access
A survey on optimal stochastic signaling and detector randomization
(IEEE, 2011) Dülek, Berkan; Göken, Çağrı; Gezici, Sinan; Arıkan, Orhan
In this paper, a survey on stochastic signaling and detector randomization is presented for average power-constrained binary communications systems. First, the case of a single fixed detector at the receiver is considered, and then the joint design of detector and optimal signaling is studied. In addition, the optimal receiver design is examined in the presence of detector randomization and stochastic signaling. It is observed that the average probability of error achieved via detector randomization cannot be larger than that achieved via stochastic signaling in the presence of optimal MAP detectors. Finally, a numerical study is presented to illustrate an example.