Browsing by Subject "Inverse problems"

Now showing 1 - 20 of 21

Open Access
Condition number in recovery of signals from partial fractional fourier domain information
(Optical Society of America, 2013-06) Oktem F. S.; Özaktaş, Haldun M.
The problem of estimating unknown signal samples from partial measurements in fractional Fourier domains arises in wave propagation. By using the condition number of the inverse problem as a measure of redundant information, we analyze the effect of the number of known samples and their distributions.
Open Access
Denoising images corrupted by impulsive noise using projections onto the epigraph set of the total variation function (PES-TV)
(Springer U K, 2015) Tofighi M.; Kose, K.; Çetin, A. Enis
In this article, a novel algorithm for denoising images corrupted by impulsive noise is presented. Impulsive noise generates pixels whose gray level values are not consistent with the neighboring pixels. The proposed denoising algorithm is a two-step procedure. In the first step, image denoising is formulated as a convex optimization problem, whose constraints are defined as limitations on local variations between neighboring pixels. We use Projections onto the Epigraph Set of the TV function (PES-TV) to solve this problem. Unlike other approaches in the literature, the PES-TV method does not require any prior information about the noise variance. It is only capable of utilizing local relations among pixels and does not fully take advantage of correlations between spatially distant areas of an image with similar appearance. In the second step, a Wiener filtering approach is cascaded to the PES-TV-based method to take advantage of global correlations in an image. In this step, the image is first divided into blocks and those with similar content are jointly denoised using a 3D Wiener filter. The denoising performance of the proposed two-step method was compared against three state-of-the-art denoising methods under various impulsive noise models.
Open Access
Dipole source reconstruction of brain signals by using particle swarm optimization
(IEEE, 2009) Alp, Yaşar Kemal; Arıkan, Orhan; Karakaş, S.
Resolving the sources of neural activity is of prime importance in the analysis of Event Related Potentials (ERP). These sources can be modeled as effective dipoles. Identifying the dipole parameters from the measured multichannel data is called the EEG inverse problem. In this work, we propose a new method for the solution of EEG inverse problem. Our method uses Particle Swarm Optimization (PSO) technique for optimally choosing the dipole parameters. Simulations on synthetic data sets show that our method well localizes the dipoles into their actual locations. In the real data sets, since the actual dipole parameters aren't known, the fit error between the measured data and the reconstructed data is minimized. It has been observed that our method reduces this error to the noise level by localizing only a few dipoles in the brain.
Open Access
Effect of different sparsity priors on compressive photon-sieve spectral imaging
(IEEE, 2018) Kar, O. F.; Oktem, F. S.; Kamaci, U.; Akyön, Fatih ÇaĞatay
Compressive spectral imaging is a rapidly growing area yielding higher performance novel spectral imagers than conventional ones. Inspired by compressed sensing theory, compressive spectral imagers aim to reconstruct the spectral images from compressive measurements using sparse signal recovery algorithms. In this paper, first, the image formation model and a sparsity-based reconstruction approach are presented for compressive photon-sieve spectral imager. Then the reconstruction performance of the approach is analyzed using different sparsity priors. In the system, a coded aperture is used for modulation and a photon-sieve for dispersion. In the measurements, coded and blurred images of spectral bands are superimposed. Simulation results show promising image reconstruction performance from these compressive measurements.
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
Exact diffraction calculation from fields specified over arbitrary curved surfaces
(Elsevier, 2011-07-30) Esmer, G. B.; Onural, L.; Özaktaş, Haldun M.
Calculation of the scalar diffraction field over the entire space from a given field over a surface is an important problem in computer generated holography. A straightforward approach to compute the diffraction field from field samples given on a surface is to superpose the emanated fields from each such sample. In this approach, possible mutual interactions between the fields at these samples are omitted and the calculated field may be significantly in error. In the proposed diffraction calculation algorithm, mutual interactions are taken into consideration, and thus the exact diffraction field can be calculated. The algorithm is based on posing the problem as the inverse of a problem whose formulation is straightforward. The problem is then solved by a signal decomposition approach. The computational cost of the proposed method is high, but it yields the exact scalar diffraction field over the entire space from the data on a surface.
Open Access
Heterogeneous multifrequency direct inversion (HMDI) for magnetic resonance elastography with application to a clinical brain exam
(Elsevier B.V., 2018) Barnhill, E.; Davies, P. J.; Ariyurek, C.; Fehlner, A.; Braun, J.; Sack, I.
A new viscoelastic wave inversion method for MRE, called Heterogeneous Multifrequency Direct Inversion (HMDI), was developed which accommodates heterogeneous elasticity within a direct inversion (DI) by incorporating first-order gradients and combining results from a narrow band of multiple frequencies. The method is compared with a Helmholtz-type DI, Multifrequency Dual Elasto-Visco inversion (MDEV), both on ground-truth Finite Element Method simulations at varied noise levels and a prospective in vivo brain cohort of 48 subjects ages 18-65. In simulated data, MDEV recovered background material within 5% and HMDI within 1% of prescribed up to SNR of 20 dB. In vivo HMDI and MDEV were then combined with segmentation from SPM to create a fully automated “brain palpation” exam for both whole brain (WB), and brain white matter (WM), measuring two parameters, the complex modulus magnitude |G*|, which measures tissue “stiffness” and the slope of |G*| values across frequencies, a measure of viscous dispersion. |G*| values for MDEV and HMDI were comparable to the literature (for a 3-frequency set centered at 50 Hz, WB means were 2.17 and 2.15 kPa respectively, and WM means were 2.47 and 2.49 kPa respectively). Both methods showed moderate correlation to age in both WB and WM, for both |G*| and |G*| slope, with Pearson's r ≥ 0.4 in the most sensitive frequency sets. In comparison to MDEV, HMDI showed better preservation of recovered target shapes, more noise-robustness, and stabler recovery values in regions with rapid property change, however summary statistics for both methods were quite similar. By eliminating homogeneity assumptions within a fast, fully automatic, regularization-free direct inversion, HMDI appears to be a worthwhile addition to the MRE image reconstruction repertoire. In addition to supporting the literature showing decrease in brain viscoelasticity with age, our work supports a wide range of inter-individual variation in brain MRE results.
Open Access
Moving region detection in compressed video
(Springer, 2004) Töreyin, B. U.; Çetin, A. Enis; Aksay, A.; Akhan, M. B.
In this paper, an algorithm for moving region detection in compressed video is developed. It is assumed that the video can be compressed either using the Discrete Cosine Transform (DOT) or the Wavelet Transform (WT). The method estimates the WT of the background scene from the WTs of the past image frames of the video. The WT of the current image is compared with the WT of the background and the moving objects are determined from the difference. The algorithm does not perform inverse WT to obtain the actual pixels of the current image nor the estimated background. In the case of DOT compressed video, the DC values of 8 by 8 image blocks of Y, U and V channels are used for estimating the background scene. This leads to a computationally efficient method and a system compared to the existing motion detection methods. © Springer-Verlag 2004.
Open Access
A novel technique for a linear system of equations applied to channel equalization
(IEEE, 2009) Pilancı, Mert; Arıkan, Orhan; Oǧuz, B.; Pınar, Mustafa Ç.
In many inverse problems of signal processing the problem reduces to a linear system of equations. Accurate and robust estimation of the solution with errors in both measurement vector and coefficient matrix is a challenging task. In this paper a novel formulation is proposed which takes into account the structure (e.g. Toeplitz, Hankel) and uncertainties of the system. A numerical algorithm is provided to obtain the solution. The proposed technique and other methods are compared in a channel equalization example which is a fundamental necessity in communication.
Open Access
Parallel preconditioners for solutions of dense linear systems with tens of millions of unknowns
(2007-11) Malas, Tahir; Ergül, Özgür; Gürel, Levent
We propose novel parallel preconditioning schemes for the iterative solution of integral equation methods. In particular, we try to improve convergence rate of the ill-conditioned linear systems formulated by the electric-field integral equation, which is the only integral-equation formulation for targets having open surfaces. For moderate-size problems, iterative solution of the near-field system enables much faster convergence compared to the widely used sparse approximate inverse preconditioner. For larger systems, we propose an approximation strategy to the multilevel fast multipole algorithm (MLFMA) to be used as a preconditioner. Our numerical experiments reveal that this scheme significantly outperforms other preconditioners. With the combined effort of effective preconditioners and an efficiently parallelized MLFMA, we are able to solve targets with tens of millions of unknowns, which are the largest problems ever reported in computational electromagnetics. ©2007 IEEE.
Open Access
Phase and TV based convex sets for blind deconvolution of microscopic images
(Institute of Electrical and Electronics Engineers Inc., 2016) Tofighi M.; Yorulmaz, O.; Köse K.; Yıldırım, D. C.; Çetin-Atalay R.; Çetin, A. Enis
In this paper, two closed and convex sets for blind deconvolution problem are proposed. Most blurring functions in microscopy are symmetric with respect to the origin. Therefore, they do not modify the phase of the Fourier transform (FT) of the original image. As a result blurred image and the original image have the same FT phase. Therefore, the set of images with a prescribed FT phase can be used as a constraint set in blind deconvolution problems. Another convex set that can be used during the image reconstruction process is the Epigraph Set of Total Variation (ESTV) function. This set does not need a prescribed upper bound on the Total Variation (TV) of the image. The upper bound is automatically adjusted according to the current image of the restoration process. Both the TV of the image and the blurring filter are regularized using the ESTV set. Both the phase information set and the ESTV are closed and convex sets. Therefore they can be used as a part of any blind deconvolution algorithm. Simulation examples are presented.
Open Access
Phase retrieval of sparse signals from Fourier Transform magnitude using non-negative matrix factorization
(IEEE, 2013) Salman, M.S.; Eleyan, A.; Deprem, Zeynel; Çetin, A. Enis
Signal and image reconstruction from Fourier Transform magnitude is a difficult inverse problem. Fourier transform magnitude can be measured in many practical applications, but the phase may not be measured. Since the autocorrelation of an image or a signal can be expressed as convolution of x(n) with x(-n), it is possible to formulate the inverse problem as a non-negative matrix factorization problem. In this paper, we propose a new algorithm based on the sparse non-negative matrix factorization (NNMF) to estimate the phase of a signal or an image in an iterative manner. Experimental reconstruction results are presented. © 2013 IEEE.
Open Access
Predicting pilot behavior in medium-scale scenarios using game theory and reinforcement learning
(American Institute of Aeronautics and Astronautics Inc., 2014) Yildiz, Y.; Agogino, A.; Brat, G.
A key element to meet the continuing growth in air traffic is the increased use of automation. Decision support systems, computer-based information acquisition, trajectory planning systems, high-level graphic display systems, and all advisory systems are considered to be automation components related to next generation (NextGen) air space. Given a set of goals represented as reward functions, the actions of the players may be predicted. However, several challenges need to be overcome. First, determining how a player can attempt to maximize their reward function can be a difficult inverse problem. Second, players may not be able to perfectly maximize their reward functions. ADS-B technology can provide pilots the information, position, velocity, etc. of other aircraft. However, a pilot has limited ability to use all this information for his/her decision making. For this scenario, the authors model these pilot limitations by assuming that pilots can observe a limited section of the grid in front of them.
Open Access
Provably optimal sparse solutions to overdetermined linear systems with non-negativity constraints in a least-squares sense by implicit enumeration
(Springer, 2021-12) Aktaş, Fatih Selim; Ekmekcioglu, Ömer; Pinar, Mustafa Çelebi
Computing sparse solutions to overdetermined linear systems is a ubiquitous problem in several fields such as regression analysis, signal and image processing, information theory and machine learning. Additional non-negativity constraints in the solution are useful for interpretability. Most of the previous research efforts aimed at approximating the sparsity constrained linear least squares problem, and/or finding local solutions by means of descent algorithms. The objective of the present paper is to report on an efficient and modular implicit enumeration algorithm to find provably optimal solutions to the NP-hard problem of sparsity-constrained non-negative least squares. We focus on the problem where the system is assumed to be over-determined where the matrix has full column rank. Numerical results with real test data as well as comparisons of competing methods and an application to hyperspectral imaging are reported. Finally, we present a Python library implementation of our algorithm.
Open Access
Randomized and rank based differential evolution
(IEEE, 2009-12) Urfalıoğlu, Onay; Arıkan, Orhan
Many real world problems which can be assigned to the machine learning domain are inverse problems. The available data is often noisy and may contain outliers, which requires the application of global optimization. Evolutionary Algorithms (EA's) are one class of possible global optimization methods for solving such problems. Within population based EA's, Differential Evolution (DE) is a widely used and successful algorithm. However, due to its differential update nature, given a current population, the set of possible new populations is finite and a true subset of the cost function domain. Furthermore, the update formula of DE does not use any information about the fitnesses of the population. This paper presents a novel extension of DE called Randomized and Rank based Differential Evolution (R2DE) to improve robustness and global convergence speed on multimodal problems by introducing two multiplicative terms in the DE update formula. The first term is based on a random variate of a Cauchy distribution, which leads to a randomization. The second term is based on ranking of individuals, so that R2DE exploits additional information provided by the fitnesses. In experiments including non-linear dimension reduction by autoencoders, it is shown that R2DE improves robustness and speed of global convergence. © 2009 IEEE.
Open Access
Reward-rate maximization in sequential identification under a stochastic deadline
(2013) Dayanık, S.; Yu, A. J.
Any intelligent system performing evidence-based decision making under time pressure must negotiate a speed-accuracy trade-off. In computer science and engineering, this is typically modeled as minimizing a Bayes-risk functional that is a linear combination of expected decision delay and expected terminal decision loss. In neuroscience and psychology, however, it is often modeled as maximizing the long-term reward rate, or the ratio of expected terminal reward and expected decision delay. The two approaches have opposing advantages and disadvantages. While Bayes-risk minimization can be solved with powerful dynamic programming techniques unlike reward-rate maximization, it also requires the explicit specification of the relative costs of decision delay and error, which is obviated by reward-rate maximization. Here, we demonstrate that, for a large class of sequential multihypothesis identification problems under a stochastic deadline, the reward-rate maximization is equivalent to a special case of Bayes-risk minimization, in which the optimal policy that attains the minimal risk when the unit sampling cost is exactly the maximal reward rate is also the policy that attains maximal reward rate. We show that the maximum reward rate is the unique unit sampling cost for which the expected total observation cost and expected terminal reward break even under every Bayes-risk optimal decision rule. This interplay between reward-rate maximization and Bayesrisk minimization formulations allows us to show that maximum reward rate is always attained. We can compute the policy that maximizes reward rate by solving an inverse Bayes-risk minimization problem, whereby we know the Bayes risk of the optimal policy and need to find the associated unit sampling cost parameter. Leveraging this equivalence, we derive an iterative dynamic programming procedure for solving the reward-rate maximization problem exponentially fast, thus incorporating the advantages of both the reward-rate maximization and Bayes-risk minimization formulations. As an illustration, we will apply the procedure to a two-hypothesis identification example.
Open Access
Self Fourier functions and fractional Fourier transforms
(Elsevier, 1994) Mendlovic, D.; Özaktaş, Haldun M.; Lohmann, A. W.
Self Fourier functions and fractional Fourier transforms are two concepts that have been discussed recently. Investigated is the combination of these two concepts: self fractional Fourier functions and the fractional Fourier transform of a self Fourier function. © 1994.
Open Access
Shape reconstruction of three-dimensional conducting objects via near-field measurements
(IEEE, 2014) Etminan, Aslan; Gürel, Levent
A general framework for the shape reconstruction of conducting objects is presented with the Newton minimization approach. Using a fully numerical method, the initial-guess object is evolved to reconstruct the target. The object is modeled by triangles such that the vertices are the unknowns of the inverse-scattering problem. The cost function is minimized as the evolving object converges to the actual target in merely tens of iterations.
Open Access
Structured least squares with bounded data uncertainties
(IEEE, 2009) Pilanci, Mert; Arıkan, Orhan; Oguz, B.; Pınar, Mustafa C.
In many signal processing applications the core problem reduces to a linear system of equations. Coefficient matrix uncertainties create a significant challenge in obtaining reliable solutions. In this paper, we present a novel formulation for solving a system of noise contaminated linear equations while preserving the structure of the coefficient matrix. The proposed method has advantages over the known Structured Total Least Squares (STLS) techniques in utilizing additional information about the uncertainties and robustness in ill-posed problems. Numerical comparisons are given to illustrate these advantages in two applications: signal restoration problem with an uncertain model and frequency estimation of multiple sinusoids embedded in white noise.
Open Access
Technique for reconstructing a surface shape for measuring coordinates
(OSA, 2006) Sainov, V. K.; Kharizanova, Z. I.; Stoikova, E. V.; Özaktaş, Haldun M.; Onural, Levent
This paper describes a method of projecting interference fringes as one of the most accessible techniques for measuring the coordinates of objects and scenes that can be used when solving inverse problems in dynamic holographic display, where the coordinates need to be measured in order to compute diffraction structures when reconstructing three-dimensional images. A comparative analysis is presented of the experimental results obtained with successive projections of interference patterns with two different periods, using a Mach-Zehnder interferometer in coherent light and a micromirror projector with digital generation of fringes in white light. The use of the method is limited by the size of the objects and scenes. The possibilities of using more refined methods, including the holographic approach to phase reconstruction, are discussed. © 2006 Optical Society of America.