Browsing by Subject "Optimal solutions"

Now showing 1 - 6 of 6

Open Access
Algebraic error analysis of collinear feature points for camera parameter estimation
(Elsevier, 2011-01-04) Urfalioglu, O.; Thormählen, T.; Broszio, H.; Mikulastik, P.; Çetin, A. Enis
In general, feature points and camera parameters can only be estimated with limited accuracy due to noisy images. In case of collinear feature points, it is possible to benefit from this geometrical regularity by correcting the feature points to lie on the supporting estimated straight line, yielding increased accuracy of the estimated camera parameters. However, regarding Maximum-Likelihood (ML) estimation, this procedure is incomplete and suboptimal. An optimal solution must also determine the error covariance of corrected features. In this paper, a complete theoretical covariance propagation analysis starting from the error of the feature points up to the error of the estimated camera parameters is performed. Additionally, corresponding Fisher Information Matrices are determined and fundamental relationships between the number and distance of collinear points and corresponding error variances are revealed algebraically. To demonstrate the impact of collinearity, experiments are conducted with covariance propagation analyses, showing significant reduction of the error variances of the estimated parameters.
Open Access
Deconvolution using projections onto the epigraph set of a convex cost function
(IEEE, 2014) Tofighi, Mohammad; Bozkurt, Alican; Köse, K.; Çetin, A. Enis
A new deconvolution algorithm based on making orthogonal projections onto the epigraph set of a convex cost function is presented. In this algorithm, the dimension of the minimization problem is lifted by one and sets corresponding to the cost function and observations are defined. If the utilized cost function is convex in RN, the corresponding epigraph set is also convex in RN+1. The deconvolution algorithm starts with an arbitrary initial estimate in RN+1. At each iteration cycle of the algorithm, first deconvolution projections are performed onto the hyperplanes representing observations, then an orthogonal projection is performed onto epigraph of the cost function. The method provides globally optimal solutions for total variation, l1, l2, and entropic cost functions.
Open Access
Minimizing weighted mean absolute deviation of job completion times from their weighted mean
(Elsevier, 2011) Erel, E.; Ghosh, J. B.
We address a single-machine scheduling problem where the objective is to minimize the weighted mean absolute deviation of job completion times from their weighted mean. This problem and its precursors aim to achieve the maximum admissible level of service equity. It has been shown earlier that the unweighted version of this problem is NP-hard in the ordinary sense. For that version, a pseudo-polynomial time dynamic program and a 2-approximate algorithm are available. However, not much (except for an important solution property) exists for the weighted version. In this paper, we establish the relationship between the optimal solution to the weighted problem and a related one in which the deviations are measured from the weighted median (rather than the mean) of the job completion times; this generalizes the 2-approximation result mentioned above. We proceed to give a pseudo-polynomial time dynamic program, establishing the ordinary NP-hardness of the problem in general. We then present a fully-polynomial time approximation scheme as well. Finally, we report the findings from a limited computational study on the heuristic solution of the general problem. Our results specialize easily to the unweighted case; they also lead to an approximation of the set of schedules that are efficient with respect to both the weighted mean absolute deviation and the weighted mean completion time. © 2011 Elsevier Inc. All rights reserved.
Open Access
Modeling of bus transit driver availability for effective emergency evacuation in disaster relief
(2013) Morgul, E.; Cavus, O.; Ozbay, K.; Iyigun, C.
Potential evacuees without access to personal automobiles are expected to use transit, especially buses, to reach safer regions. For a transit agency, operation problems to be considered include establishing bus launch areas, positioning the minimum number of required buses, and coordinating transit operators, especially determining whether the number of drivers will be sufficient to cover the number of vehicles (i.e., buses) to be used during the evacuation. It is also highly probable that during an emergency, absenteeism rates for bus drivers might increase. In this study, the authors developed two stochastic models to determine the need for extra drivers during an emergency evacuation and to provide optimal solutions using well-established concepts in mathematical programming. First, the authors reviewed the literature to develop an effective methodology for the development of optimal extraboard management strategies. The authors found that although several recent reports clearly mentioned the problem of not having enough bus drivers during emergency evacuation operations, no analytical study incorporated the optimal extraboard size problem into emergency evacuation operations. Second, two mathematical models are presented in this paper. The aim of the developed models is to fill the gap in the literature for determining optimal extraboard size for transit operations during emergency evacuations. The models are specifically designed to capture risk-averse behavior of decision makers. Finally, these models were tested with hypothetical examples from real-world data from New Jersey. Results show that both models give reasonable extraboard size estimates, and under different conditions, these models are responsive to the changes in cost and quality of service preferences. The results are encouraging in terms of the models' usefulness for real-world applications.
Open Access
Optimal signaling and detector design for power constrained on-off keying systems in Neyman-Pearson framework
(IEEE, 2011) Dulek, Berkan; Gezici, Sinan
Optimal stochastic signaling and detector design are studied for power constrained on-off keying systems in the presence of additive multimodal channel noise under the Neyman-Pearson (NP) framework. The problem of jointly designing the signaling scheme and the decision rule is addressed in order to maximize the probability of detection without violating the constraints on the probability of false alarm and the average transmit power. Based on a theoretical analysis, it is shown that the optimal solution can be obtained by employing randomization between at most two signal values for the on-signal (symbol 1) and using the corresponding NP-type likelihood ratio test at the receiver. As a result, the optimal parameters can be computed over a significantly reduced optimization space instead of an infinite set of functions using global optimization techniques. Finally, a detection example is provided to illustrate how stochastic signaling can help improve detection performance over various optimal and sub-optimal signaling schemes. © 2011 IEEE.
Open Access
Ultra-wideband orthogonal pulse shape set design by using Hermite-Gaussian functions
(IEEE, 2012) Alp, Yaşar Kemal; Dedeoǧlu, Mehmet; Arıkan, Orhan
Ultra-Wideband (UWB) communication systems have been developed for short distance, high data rate communications. To avoid interfering with the existing systems in the same environment, very short duration pulses used by these systems should satisfy a predefined spectral mask. Data rate of UWB systems can be increased by using multiple pulse shapes simultaneously. Orthogonality of the simultaneously used pulse shapes simplifies the receiver design. In this work, design of orthogonal pulse shapes which satisfy the spectral mask is modelled as an optimization problem. First, it is converted to a convex optimization problem by constraining the pulse shapes to lie in a subspace spanned by the Hermite-Gaussian (HG) functions. Then the optimal solution is obtained. It is shown that a larger pulse shape set can be designed compared to the existing approaches, and hence, a higher data rate can be achieved. © 2012 IEEE.