Browsing by Subject "Maximum principle"

Now showing 1 - 5 of 5

Open Access
Bohr phenomena for Laplace-Beltrami operators
(2006) Kaptanoğlu, Hakkı Turgay
We investigate a Bohr phenomenon on the spaces of solutions of weighted Laplace-Beltrami operators associated with the hyperbolic metric of the unit ball in ℂN. These solutions do not satisfy the usual maximum principle, and the spaces have natural bases none of whose members is a constant function. We show that these bases exhibit a Bohr phenomenon, define a Bohr radius for them that extends the classical Bohr radius, and compute it exactly. We also compute the classical Bohr radius of the invariant harmonic functions on the real hyperbolic space.
Open Access
Expectation maximization based matching pursuit
(IEEE, 2012) Gurbuz, A.C.; Pilanci, M.; Arıkan, Orhan
A novel expectation maximization based matching pursuit (EMMP) algorithm is presented. The method uses the measurements as the incomplete data and obtain the complete data which corresponds to the sparse solution using an iterative EM based framework. In standard greedy methods such as matching pursuit or orthogonal matching pursuit a selected atom can not be changed during the course of the algorithm even if the signal doesn't have a support on that atom. The proposed EMMP algorithm is also flexible in that sense. The results show that the proposed method has lower reconstruction errors compared to other greedy algorithms using the same conditions. © 2012 IEEE.
Open Access
Extraction of primary and secondary frequency control from active power generation data of power plants
(Elsevier Ltd, 2015) Ozer, B.; Arıkan, Orhan; Moral, G.; Altintas, A.
Frequency control is a vital component of a secure and robust power grid and it ought to be closely monitored. Frequency control consists of two main components; primary and secondary control and their contributions are usually aggregated in the active power generation data of a plant, which is acquired via Supervisory Control And Data Acquisition. In many cases, such as in Turkey, they are demanded to be evaluated separately due to different impacts on power system or different financial policies. However, this is not usually a straightforward process since primary and secondary response cannot be obtained distinctly. In this work, Extraction of Primary and Secondary Control (EPSCon) algorithm is introduced to extract primary and secondary response over active power generation data. Based on time and frequency domain characteristics of primary and secondary response, EPSCon is developed on a Expectation-Maximization type recursive scheme employing Generalized Cross Correlation and ℓ1 Trend Filtering techniques. Favorably, EPSCon uses a simple plant model built upon basic governor and plant load controller technical characteristics as an initial estimate of primary and secondary response.
Open Access
A recursive way for sparse reconstruction of parametric spaces
(IEEE, 2015-11) Teke, Oğuzhan; Gürbüz, A. C.; Arıkan, Orhan
A novel recursive framework for sparse reconstruction of continuous parameter spaces is proposed by adaptive partitioning and discretization of the parameter space together with expectation maximization type iterations. Any sparse solver or reconstruction technique can be used within the proposed recursive framework. Experimental results show that proposed technique improves the parameter estimation performance of classical sparse solvers while achieving Cramér-Rao lower bound on the tested frequency estimation problem. © 2014 IEEE.
Open Access
SAR image reconstruction by expectation maximization based matching pursuit
(Academic Press, 2015) Ugur, S.; Arıkan, Orhan; Gürbüz, A. C.
Synthetic Aperture Radar (SAR) provides high resolution images of terrain and target reflectivity. SAR systems are indispensable in many remote sensing applications. Phase errors due to uncompensated platform motion degrade resolution in reconstructed images. A multitude of autofocusing techniques has been proposed to estimate and correct phase errors in SAR images. Some autofocus techniques work as a post-processor on reconstructed images and some are integrated into the image reconstruction algorithms. Compressed Sensing (CS), as a relatively new theory, can be applied to sparse SAR image reconstruction especially in detection of strong targets. Autofocus can also be integrated into CS based SAR image reconstruction techniques. However, due to their high computational complexity, CS based techniques are not commonly used in practice. To improve efficiency of image reconstruction we propose a novel CS based SAR imaging technique which utilizes recently proposed Expectation Maximization based Matching Pursuit (EMMP) algorithm. EMMP algorithm is greedy and computationally less complex enabling fast SAR image reconstructions. The proposed EMMP based SAR image reconstruction technique also performs autofocus and image reconstruction simultaneously. Based on a variety of metrics, performance of the proposed EMMP based SAR image reconstruction technique is investigated. The obtained results show that the proposed technique provides high resolution images of sparse target scenes while performing highly accurate motion compensation.