Browsing by Subject "Iterative methods"

Now showing 1 - 20 of 79

Open Access
Adaptive power control and MMSE interference suppression
(1998) Ulukus, S.; Yates, R.D.
Power control algorithms assume that the receiver structure is fixed and iteratively update the transmit powers of the users to provide acceptable quality of service while minimizing the total transmitter power. Multiuser detection, on the other hand, optimizes the receiver structure with the assumption that the users have fixed transmitter powers. In this study, we combine the two approaches and propose an iterative and distributed power control algorithm which iteratively updates the transmitter powers and receiver filter coefficients of the users. We show that the algorithm converges to a minimum power solution for the powers, and an MMSE multiuser detector for the filter coefficients.
Open Access
Analyzing large sparse Markov chains of Kronecker products
(IEEE, 2009) Dayar, Tuğrul
Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. In the Kronecker based approach, the generator matrix underlying the MC is represented using Kronecker products [6] of smaller matrices and is never explicitly generated. The implementation of transient and steady-state solvers rests on this compact Kronecker representation, thanks to the existence of an efficient vector-Kronecker product multiplication algorithm known as the shuffle algorithm [6]. The transient distribution can be computed through uniformization using vector-Kronecker product multiplications. The steady-state distribution also needs to be computed using vector-Kronecker product multiplications, since direct methods based on complete factorizations, such as Gaussian elimination, normally introduce new nonzeros which cannot be accommodated. The two papers [2], [10] provide good overviews of iterative solution techniques for the analysis of MCs based on Kronecker products. Issues related to reachability analysis, vector-Kronecker product multiplication, hierarchical state space generation in Kronecker based matrix representations for large Markov models are surveyed in [5]. Throughout our discussion, we make the assumption that the MC at hand does not have unreachable states, meaning it is irreducible. And we take an algebraic view [7] to discuss recent results related to the analysis of MCs based on Kronecker products independently from modeling formalisms. We provide background material on the Kronecker representation of the generator matrix underlying a CTMC, show that it has a rich structure which is nested and recursive, and introduce a small CTMC whose generator matrix is expressed as a sum of Kronecker products; this CTMC is used as a running example throughout the discussion. We also consider preprocessing of the Kronecker representation so as to expedite numerical analysis. We discuss permuting the nonzero structure of the underlying CTMC symmetrically by reordering, changing the orders of the nested blocks by grouping, and reducing the size of the state space by lumping. The steady-state analysis of CTMCs based on Kronecker products is discussed for block iterative methods, multilevel methods, and preconditioned projection methods, respectively. The results can be extended to DTMCs based on Kronecker products with minor modifications. Areas that need further research are mentioned as they are discussed. Our contribution to this area over the years corresponds to work along iterative methods based on splittings and their block versions [11], associated preconditioners to be used with projection methods [4], near complete decomposability [8], a method based on iterative disaggregation for a class of lumpable MCs [9], a class of multilevel methods [3], and a recent method based on decomposition for weakly interacting subsystems [1]. © 2009 IEEE.
Open Access
Auto-tuning similarity search algorithms on multi-core architectures
(2013) Gedik, B.
In recent times, large high-dimensional datasets have become ubiquitous. Video and image repositories, financial, and sensor data are just a few examples of such datasets in practice. Many applications that use such datasets require the retrieval of data items similar to a given query item, or the nearest neighbors (NN or k -NN) of a given item. Another common query is the retrieval of multiple sets of nearest neighbors, i.e., multi k -NN, for different query items on the same data. With commodity multi-core CPUs becoming more and more widespread at lower costs, developing parallel algorithms for these search problems has become increasingly important. While the core nearest neighbor search problem is relatively easy to parallelize, it is challenging to tune it for optimality. This is due to the fact that the various performance-specific algorithmic parameters, or "tuning knobs", are inter-related and also depend on the data and query workloads. In this paper, we present (1) a detailed study of the various tuning knobs and their contributions on increasing the query throughput for parallelized versions of the two most common classes of high-dimensional multi-NN search algorithms: linear scan and tree traversal, and (2) an offline auto-tuner for setting these knobs by iteratively measuring actual query execution times for a given workload and dataset. We show experimentally that our auto-tuner reaches near-optimal performance and significantly outperforms un-tuned versions of parallel multi-NN algorithms for real video repository data on a variety of multi-core platforms. © 2013 Springer Science+Business Media New York.
Open Access
Combined-field solution of composite geometries involving open and closed conducting surfaces
(IEEE, 2005-04) Ergül, Özgür; Gürel, Levent
Combined-field integral equation (CFIE) is modified and generalized to formulate the electromagnetic problems of composite geometries involving both open and closed conducting surfaces. These problems are customarily formulated with the electric-field integral equation (EFIE) due to the presence of the open surfaces. With the new definition and application of the CFIE, iterative solutions of these problems are now achieved with significantly improved efficiency compared to the EFIE solution, without sacrificing the accuracy. © 2005 ACES.
Open Access
Comparisons of FMM implementations employing different formulations and iterative solvers
(IEEE, 2003-06) Gürel, Levent; Ergül, Özgür
The implementation of multi-level fast multipole algorithm (MLFMA) requires the consideration of several parameters. The preferred combination of the parameters given is not trivially obvious and requires a careful investigation. This paper extensively investigates such parameters by using a series of scattering problems of various sizes containing different numbers of unknowns as a testbed.
Open Access
A complexity-reduced ML parametric signal reconstruction method
(2011) Deprem, Z.; Leblebicioglu, K.; Arkan O.; Çetin, A.E.
The problem of component estimation from a multicomponent signal in additive white Gaussian noise is considered. A parametric ML approach, where all components are represented as a multiplication of a polynomial amplitude and polynomial phase term, is used. The formulated optimization problem is solved via nonlinear iterative techniques and the amplitude and phase parameters for all components are reconstructed. The initial amplitude and the phase parameters are obtained via time-frequency techniques. An alternative method, which iterates amplitude and phase parameters separately, is proposed. The proposed method reduces the computational complexity and convergence time significantly. Furthermore, by using the proposed method together with Expectation Maximization (EM) approach, better reconstruction error level is obtained at low SNR. Though the proposed method reduces the computations significantly, it does not guarantee global optimum. As is known, these types of non-linear optimization algorithms converge to local minimum and do not guarantee global optimum. The global optimum is initialization dependent. © 2011 Z. Deprem et al.
Open Access
Compressive sensing-based robust off-the-grid stretch processing
(Institution of Engineering and Technology, 2017) Ilhan, I.; Gurbuz, A. C.; Arıkan, Orhan
Classical stretch processing (SP) obtains high range resolution by compressing large bandwidth signals with narrowband receivers using lower rate analogue-to-digital converters. SP achieves the resolution of the large bandwidth signal by focusing into a limited range window, and by deramping in the analogue domain. SP offers moderate data rate for signal processing for high bandwidth waveforms. Furthermore, if the scene in the examined window is sparse, compressive sensing (CS)-based techniques have the potential to further decrease the required number of measurements. However, CS-based reconstructions are highly affected by model mismatches such as targets that are off-the-grid. This study proposes a sparsity-based iterative parameter perturbation technique for SP that is robust to targets off-the-grid in range or Doppler. The error between reconstructed and actual scenes is measured using Earth mover's distance metric. Performance analyses of the proposed technique are compared with classical CS and SP techniques in terms of data rate, resolution and signal-to-noise ratio. It is shown through simulations that the proposed technique offers robust and high-resolution reconstructions for the same data rate compared with both classical SP- and CS-based techniques.
Open Access
Contamination of the accuracy of the combined-field integral equation with the discretization error of the magnetic-field integral equation
(Institute of Electrical and Electronics Engineers, 2009) Gürel, Levent; Ergül, Özgür
We investigate the accuracy of the combined-field integral equation (CFIE) discretized with the Rao-Wilton-Glisson (RWG) basis functions for the solution of scattering and radiation problems involving three-dimensional conducting objects. Such a low-order discretization with the RWG functions renders the two components of CFIE, i.e., the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE), incompatible, mainly because of the excessive discretization error of MFIE. Solutions obtained with CFIE are contaminated with the MFIE inaccuracy, and CFIE is also incompatible with EFIE and MFIE. We show that, in an iterative solution, the minimization of the residual error for CFIE involves a breakpoint, where a further reduction of the residual error does not improve the solution in terms of compatibility with EFIE, which provides a more accurate reference solution. This breakpoint corresponds to the last useful iteration, where the accuracy of CFIE is saturated and a further reduction of the residual error is practically unnecessary.
Open Access
Data imputation through the identification of local anomalies
(Institute of Electrical and Electronics Engineers Inc., 2015) Ozkan, H.; Pelvan, O. S.; Kozat, S. S.
We introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources, e.g., an occluder in the case of a visual recording. Within this framework, we propose: 1) a novel algorithm to efficiently separate, i.e., detect and localize, possible corruptions from a given suspicious data instance and 2) a maximum a posteriori estimator to impute the corrupted data. As a generalization to Euclidean distance, we also propose a novel distance measure, which is based on the ranked deviations among the data attributes and empirically shown to be superior in separating the corruptions. Our algorithm first splits the suspicious instance into parts through a binary partitioning tree in the space of data attributes and iteratively tests those parts to detect local anomalies using the nominal statistics extracted from an uncorrupted (clean) reference data set. Once each part is labeled as anomalous versus normal, the corresponding binary patterns over this tree that characterize corruptions are identified and the affected attributes are imputed. Under a certain conditional independency structure assumed for the binary patterns, we analytically show that the false alarm rate of the introduced algorithm in detecting the corruptions is independent of the data and can be directly set without any parameter tuning. The proposed framework is tested over several well-known machine learning data sets with synthetically generated corruptions and experimentally shown to produce remarkable improvements in terms of classification purposes with strong corruption separation capabilities. Our experiments also indicate that the proposed algorithms outperform the typical approaches and are robust to varying training phase conditions. © 2015 IEEE.
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
Denoising using projections onto the epigraph set of convex cost functions
(IEEE, 2014) Tofighi, Mohammad; Köse, K.; Çetin, A. Enis
A new denoising algorithm based on 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 feasibility sets corresponding to the cost function using the epigraph concept are defined. As the utilized cost function is a convex function in RN, the corresponding epigraph set is also a convex set in RN+1. The denoising algorithm starts with an arbitrary initial estimate in RN+1. At each step of the iterative denoising, an orthogonal projection is performed onto one of the constraint sets associated with the cost function in a sequential manner. The method provides globally optimal solutions for total-variation, ℓ1, ℓ2, and entropic cost functions.1
Open Access
Design and analysis of a modular learning based cross-coupled control algorithm for multi-axis precision positioning systems
(Institute of Control, Robotics and Systems, 2016) Ulu, N. G.; Ulu E.; Cakmakci, M.
Increasing demand for micro/nano-technology related equipment resulted in growing interest for precision positioning systems. In this paper a modular controller combining cross-coupled control and iterative learning control approaches to improve contour and tracking accuracy at the same time is presented. Instead of using the standard error estimation technique, a computationally efficient and modular contour error estimation technique is used. The new controller is more suitable for tracking arbitrary nonlinear contours and easier to implement to multi-axis systems. Stability and convergence analysis for the proposed controller is presented with the necessary conditions. Effectiveness of the control design is verified with simulations and experiments on a two-axis positioning system. The resulting positioning system achieves nanometer level contouring and tracking performance. © 2016, Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg.
Open Access
Downlink beamforming under individual SINR and per antenna power constraints
(IEEE, 2007-08) Yazarel, Y. K.; Aktaş, Defne
In this paper we consider the problem of finding the optimum beamforming vectors for the downlink of a multiuser system, where there are individual signal to interference plus noise ratio (SINR) targets for each user. Majority of the previous work on this problem assumed a total power constraint on the base stations. However, since each transmit antenna is limited by the amount of power it can transmit due to the limited linear region of the power amplifliers, a more realistic constraint is to place a limit on the per antenna power. In a recent work, Yu and Lan proposed an iterative algorithm for computing the optimum beamforming vectors minimizing the power margin over all antennas under individual SINR and per antenna power constraints. However, from a system designer point of view, it may be more desirable to minimize the total transmit power rather than minimizing the power margin, especially when the system is not symmetric. Reformulating the transmitter optimization problem to minimize the total transmit power subject to individual SINR constraints on the users and per antenna power constraints on the base stations, the algorithm proposed by Yu and Lan is modified. Performance of the modified algorithm is compared with existing methods for various cellular array scenarios. ©2007 IEEE.
Open Access
Efficient analysis of large phased arrays using iterative MoM with DFT-based acceleration algorithm
(John Wiley & Sons, Inc., 2003) Ertürk, V. B.; Chou, H-T.
A discrete Fourier transform (DFT)-based iterative method of moments (IMoM) algorithm is developed to provide an O(Ntot) computational complexity and memory storages for the efficient analysis of electromagnetic radiation/scattering from large phased arrays. Here, Ntot is the total number of unknowns. Numerical results for both printed and free-standing dipole arrays are presented to validate the algorithm's efficiency and accuracy.
Open Access
Electromagnetic imaging of three-dimensional dielectric objects with Newton minimization
(IEEE, 2014) Etminan, Aslan; Sadeghi, Alireza; Gürel, Levent
We present a general framework for detecting the shape and electrical properties of unknown objects by using the Newton minimization approach for solving inverse-scattering problems. This procedure is performed by evolving an initial-guess object iteratively until the cost function decreases to a desired value. Rapid convergence of this method is demonstrated by some numerical results.
Open Access
Encapsulating multiple communication-cost metrics in partitioning sparse rectangular matrices for parallel matrix-vector multiplies
(SIAM, 2004) Uçar, B.; Aykanat, Cevdet
This paper addresses the problem of one-dimensional partitioning of structurally unsymmetric square and rectangular sparse matrices for parallel matrix-vector and matrix-transpose-vector multiplies. The objective is to minimize the communication cost while maintaining the balance on computational loads of processors. Most of the existing partitioning models consider only the total message volume hoping that minimizing this communication-cost metric is likely to reduce other metrics. However, the total message latency (start-up time) may be more important than the total message volume. Furthermore, the maximum message volume and latency handled by a single processor are also important metrics. We propose a two-phase approach that encapsulates all these four communication-cost metrics. The objective in the first phase is to minimize the total message volume while maintaining the computational-load balance. The objective in the second phase is to encapsulate the remaining three communication-cost metrics. We propose communication-hypergraph and partitioning models for the second phase. We then present several methods for partitioning communication hypergraphs. Experiments on a wide range of test matrices show that the proposed approach yields very effective partitioning results. A parallel implementation on a PC cluster verifies that the theoretical improvements shown by partitioning results hold in practice.
Open Access
Equiripple FIR filter design by the FFT algorithm
(Institute of Electrical and Electronics Engineers, 1997-03) Çetin, A. Enis; Gerek, Ö. N.; Yardımcı, Y.
The fast Fourier transform (FFT) algorithm has been used in a variety of applications in signal and image processing. In this article, a simple procedure for designing finite-extent impulse response (FIR) discrete-time filters using the FFT algorithm is described. The zero-phase (or linear phase) FIR filter design problem is formulated to alternately satisfy the frequency domain constraints on the magnitude response bounds and time domain constraints on the impulse response support. The design scheme is iterative in which each iteration requires two FFT computations. The resultant filter is an equiripple approximation to the desired frequency response. The main advantage of the FFT-based design method is its implementational simplicity and versatility. Furthermore, the way the algorithm works is intuitive and any additional constraint can be incorporated in the iterations, as long as the convexity property of the overall operations is preserved. In one-dimensional cases, the most widely used equiripple FIR filter design algorithm is the Parks-McClellan algorithm (1972). This algorithm is based on linear programming, and it is computationally efficient. However, it cannot be generalized to higher dimensions. Extension of our design method to higher dimensions is straightforward. In this case two multidimensional FFT computations are needed in each iteration.
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
Extending the applicability of the combined-field integral equation to geometries containing open surfaces
(Institute of Electrical and Electronics Engineers, 2006) Gürel, Levent; Ergül, Özgür
In this letter, we consider the solution of large electromagnetics problems of composite structures with coexisting open and closed conductors. By modifying the construction of the combined-field integral equation (CFIE), we demonstrate a significant improvement in the iterative solution of these problems compared to the conventional electric-field formulation.
Open Access
FAME: Face association through model evolution
(IEEE, 2015-06) Gölge, Eren; Duygulu, Pınar
We attack the problem of building classifiers for public faces from web images collected through querying a name. The search results are very noisy even after face detection, with several irrelevant faces corresponding to other people. Moreover, the photographs are taken in the wild with large variety in poses and expressions. We propose a novel method, Face Association through Model Evolution (FAME), that is able to prune the data in an iterative way, for the models associated to a name to evolve. The idea is based on capturing discriminative and representative properties of each instance and eliminating the outliers. The final models are used to classify faces on novel datasets with different characteristics. On benchmark datasets, our results are comparable to or better than the state-of-the-art studies for the task of face identification. © 2015 IEEE.