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Item Open Access Accelerated phase-cycled SSFP imaging with compressed sensing(Institute of Electrical and Electronics Engineers Inc., 2015) Çukur, T.Show more Balanced steady-state free precession (SSFP) imaging suffers from irrecoverable signal losses, known as banding artifacts, in regions of large B0 field inhomogeneity. A common solution is to acquire multiple phase-cycled images each with a different frequency sensitivity, such that the location of banding artifacts are shifted in space. These images are then combined to alleviate signal loss across the entire field-of-view. Although high levels of artifact suppression are viable using a large number of images, this is a time costly process that limits clinical utility. Here, we propose to accelerate individual acquisitions such that the overall scan time is equal to that of a single SSFP acquisition. Aliasing artifacts and noise are minimized by using a variable-density random sampling pattern in k-space, and by generating disjoint sampling patterns for separate acquisitions. A sparsity-enforcing method is then used for image reconstruction. Demonstrations on realistic brain phantom images, and in vivo brain and knee images are provided. In all cases, the proposed technique enables robust SSFP imaging in the presence of field inhomogeneities without prolonging scan times. © 2014 IEEE.Show more Item Open Access Average error in recovery of sparse signals and discrete fourier transform(IEEE, 2012-04) Özçelikkale, Ayça; Yüksel, S.; Özaktaş Haldun M.Show more In compressive sensing framework it has been shown that a sparse signal can be successfully recovered from a few random measurements. The Discrete Fourier Transform (DFT) is one of the transforms that provide the best performance guarantees regardless of which components of the signal are nonzero. This result is based on the performance criterion of signal recovery with high probability. Whether the DFT is the optimum transform under average error criterion, instead of high probability criterion, has not been investigated. Here we consider this optimization problem. For this purpose, we model the signal as a random process, and propose a model where the covariance matrix of the signal is used as a measure of sparsity. We show that the DFT is, in general, not optimal despite numerous results that suggest otherwise. © 2012 IEEE.Show more Item Open Access Compressed sensing on ambiguity function domain for high resolution detection(IEEE, 2010) Güldoǧan, Mehmet B.; Pilancı, Mert; Arıkan, OrhanShow more In this paper, by using compressed sensing techniques, a new approach to achieve robust high resolution detection in sparse multipath channels is presented. Currently used sparse reconstruction techniques are not immediately applicable in wireless channel modeling and radar signal processing. Here, we make use of the cross-ambiguity function (CAF) and transformed the reconstruction problem from time to delay-Doppler domain for efficient exploitation of the delay-Doppler diversity of the multipath components. Simulation results quantify the performance gain and robustness obtained by this new CAF based compressed sensing approach. ©2010 IEEE.Show more Item Open Access A compression method for 3-D laser range scans of indoor environments based on compressive sensing(IEEE, 2011-08-09) Dobrucalı, Oğuzcan; Barshan, BiilurShow more Modeling and representing 3-D environments require the transmission and storage of vast amount of measurements that need to be compressed efficiently. We propose a novel compression technique based on compressive sensing for 3-D range measurements that are found to be correlated with each other. The main issue here is finding a highly sparse representation of the range measurements, since they do not have highly sparse representations in common domains, such as the frequency domain. To solve this problem, we generate sparse innovations between consecutive range measurements along the axis of the sensor's motion. We obtain highly sparse innovations compared with other possible ones generated by estimation and filtering. Being a lossy technique, the proposed method performs reasonably well compared with widely used compression techniques. © 2011 EURASIP.Show more Item Open Access Compressive sampling and adaptive multipath estimation(IEEE, 2010) Pilancı, Mert; Arıkan, OrhanShow more In many signal processing problems such as channel estimation and equalization, the problem reduces to a linear system of equations. In this proceeding we formulate and investigate linear equations systems with sparse perturbations on the coefficient matrix. In a large class of matrices, it is possible to recover the unknowns exactly even if all the data, including the coefficient matrix and observation vector is corrupted. For this aim, we propose an optimization problem and derive its convex relaxation. The numerical results agree with the previous theoretical findings of the authors. The technique is applied to adaptive multipath estimation in cognitive radios and a significant performance improvement is obtained. The fact that rapidly varying channels are sparse in delay and doppler domain enables our technique to maintain reliable communication even far from the channel training intervals. ©2010 IEEE.Show more Item Open Access Compressive sensing based flame detection in infrared videos(IEEE, 2013) Günay, Osman; Çetin, A. EnisShow more In this paper, a Compressive Sensing based feature extraction algorithm is proposed for flame detection using infrared cameras. First, bright and moving regions in videos are detected. Then the videos are divided into spatio-temporal blocks and spatial and temporal feature vectors are exctracted from these blocks. Compressive Sensing is used to exctract spatial feature vectors. Compressed measurements are obtained by multiplying the pixels in the block with the sensing matrix. A new method is also developed to generate the sensing matrix. A random vector generated according to standard Gaussian distribution is passed through a wavelet transform and the resulting matrix is used as the sensing matrix. Temporal features are obtained from the vector that is formed from the difference of mean intensity values of the frames in two neighboring blocks. Spatial feature vectors are classified using Adaboost. Temporal feature vectors are classified using hidden Markov models. To reduce the computational cost only moving and bright regions are classified and classification is performed at specified intervals instead of every frame. © 2013 IEEE.Show more Item Open Access Compressive sensing based target detection in delay-doppler radars(IEEE, 2013) Teke, Oguzhan; Arıkan, Orhan; Gürbüz, A.C.Show more Compressive Sensing theory shows that, a sparse signal can be reconstructed from its sub-Nyquist rate random samples. With this property, CS approach has many applications. Radar systems, which deal with sparse signal due to its nature, is one of the important application of CS theory. Even if CS approach is suitable for radar systems, classical detections schemes under Neyman-Pearson formulations may result high probability of false alarm, when CS approach is used, especially if the target has off-grid parameters. In this study, a new detection scheme which enables CS techniques to be used in radar systems is investigated. © 2013 IEEE.Show more Item Open Access Compressive sensing imaging with a graphene modulator at THz frequency in transmission mode(IEEE, 2016) Özkan, V. A.; Takan, T.; Kakenov, Nurbek; Kocabaş, Coşkun; Altan, H.Show more In this study we demonstrate compressive sensing imaging with a unique graphene based optoelectronic device which allows us to modulate the THz field through an array of columns or rows distributed throughout its face.Show more Item Open Access Detection of sparse targets with structurally perturbed echo dictionaries(Elsevier, 2013) Guldogan, M. B.; Arıkan, OrhanShow more In this paper, a novel algorithm is proposed to achieve robust high resolution detection in sparse multipath channels. Currently used sparse reconstruction techniques are not immediately applicable in multipath channel modeling. Performance of standard compressed sensing formulations based on discretization of the multipath channel parameter space degrade significantly when the actual channel parameters deviate from the assumed discrete set of values. To alleviate this off-grid problem, we make use of the particle swarm optimization (PSO) to perturb each grid point that reside in each multipath component cluster. Orthogonal matching pursuit (OMP) is used to reconstruct sparse multipath components in a greedy fashion. Extensive simulation results quantify the performance gain and robustness obtained by the proposed algorithm against the off-grid problem faced in sparse multipath channels.Show more Item Open Access Ellipsoid genişletmeyle seyrek sinyal geri oluşturma(IEEE, 2011-04) Gürbüz, A. C.; Pilancı, M.; Arıkan, OrhanShow more Bu makalede b = Ax + n şeklinde gürültülü A’nın tam rank ve x’in seyrek olduğu doğrusal bir denklem sistemi için seyrek x sinyallerini doğru olarak geri oluşturmaya yönelik yeni bir yöntem sunulmuştur. Önerilen yöntem kullanılan veri sınırını belirleyen ||Ax − b||2 = ellipsoidinin genişletilirken sırayla eksenlerin sıfırlanmasına dayanan yinelemeli bir yöntemdir. Seyrek sinyal oluşturma alanında yinelemeli ve 1 norm minimizasyon tabanlı standard yöntemlere göre benzer problemlerde daha yüksek başarım gösteren metot, eksik belirtilmiş sistemlerde standard metotların oluşturması gereken seyreklik seviyesini de yumuşatmaktadırShow more Item Open Access An empirical eigenvalue-threshold test for sparsity level estimation from compressed measurements(IEEE, 2014) Lavrenko, A.; Römer, F.; Del Galdo, G.; Thoma, R.; Arıkan, OrhanShow more Compressed sensing allows for a significant reduction of the number of measurements when the signal of interest is of a sparse nature. Most computationally efficient algorithms for signal recovery rely on some knowledge of the sparsity level, i.e., the number of non-zero elements. However, the sparsity level is often not known a priori and can even vary with time. In this contribution we show that it is possible to estimate the sparsity level directly in the compressed domain, provided that multiple independent observations are available. In fact, one can use classical model order selection algorithms for this purpose. Nevertheless, due to the influence of the measurement process they may not perform satisfactorily in the compressed sensing setup. To overcome this drawback, we propose an approach which exploits the empirical distributions of the noise eigenvalues. We demonstrate its superior performance compared to state-of-the-art model order estimation algorithms numerically.Show more Item Open Access Image feature extraction using compressive sensing(Springer, 2014) Eleyan, A.; Köse, Kıvanç; Çetin, A. EnisShow more In this paper a new approach for image feature extraction is presented. We used the Compressive Sensing (CS) concept to generate the measurement matrix. The new measurement matrix is different from the measurement matrices in literature as it was constructed using both zero mean and nonzero mean rows. The image is simply projected into a new space using the measurement matrix to obtain the feature vector. Another proposed measurement matrix is a random matrix constructed from binary entries. Face recognition problem was used as an example for testing the feature extraction capability of the proposed matrices. Experiments were carried out using two well-known face databases, namely, ORL and FERET databases. System performance is very promising and comparable with the classical baseline feature extraction algorithms.Show more Item Open Access Performance assessment of a diffraction field computation method based on source model(IEEE, 2008-05) Esmer, G. Bora; Onural, Levent; Özaktaş, Haldun M.; Uzunov, V.; Gotchev, A.Show more Efficient computation of scalar optical diffraction field due to an object is an essential issue in holographic 3D television systems. The first step in the computation process is to construct an object. As a solution for this step, we assume that an object can be represented by a set of distributed data points over a space. The second step is to determine which algorithm provides better performance. The source model whose performance is investigated is based on superposition of the diffraction fields emanated from the hypothetical light sources located at the given sample points. Its performance is evaluated according to visual quality of the reconstructed field and its algorithmic complexity. Source model provides acceptable reconstructed patterns when the region in which the samples are given has a narrow depth along the longitudinal direction and a wide extent along the transversal directions. Also, the source model gives good results when the cumulative field at the location of each point due to all other sources tends to be independent of that location. ©2008 IEEE.Show more Item Open Access Perturbed orthogonal matching pursuit(IEEE, 2013) Teke, O.; Gurbuz, A. C.; Arıkan, OrhanShow more Compressive Sensing theory details how a sparsely represented signal in a known basis can be reconstructed with an underdetermined linear measurement model. However, in reality there is a mismatch between the assumed and the actual bases due to factors such as discretization of the parameter space defining basis components, sampling jitter in A/D conversion, and model errors. Due to this mismatch, a signal may not be sparse in the assumed basis, which causes significant performance degradation in sparse reconstruction algorithms. To eliminate the mismatch problem, this paper presents a novel perturbed orthogonal matching pursuit (POMP) algorithm that performs controlled perturbation of selected support vectors to decrease the orthogonal residual at each iteration. Based on detailed mathematical analysis, conditions for successful reconstruction are derived. Simulations show that robust results with much smaller reconstruction errors in the case of perturbed bases can be obtained as compared to standard sparse reconstruction techniques.Show more Item Open Access Polar compressive sampling: A novel technique using polar codes(IEEE, 2010) Pilancı, Mert; Arıkan, Orhan; Arıkan, ErdalShow more Recently introduced Polar coding is the first practical coding technique that can be proven to achieve the Shannon capacity for a multitude of communication channels. Polar codes are close to Reed-Muller codes except the fact that they are tuned for the parameters of the channel. Hence, Polar codes are shown to offer better performance, e.g., in the erasure channel. It is known that second order Reed-Muller codes can be used for Compressed Sensing. Inspired by that result, we propose Polar codes as measurement matrices in CS and compare their numerical performances. We also present the algebraic relation between the erasure channel and CS theory, and discuss fast solution techniques. ©2010 IEEE.Show more Item Open Access Range-doppler radar target detection using denoising within the compressive sensing framework(IEEE, 2014-09) Sevimli, R. Akın; Tofighi, Mohammad; Çetin, A. EnisShow more Compressive sensing (CS) idea enables the reconstruction of a sparse signal from a small set of measurements. CS approach has applications in many practical areas. One of the areas is radar systems. In this article, the radar ambiguity function is denoised within the CS framework. A new denoising method on the projection onto the epigraph set of the convex function is also developed for this purpose. This approach is compared to the other CS reconstruction algorithms. Experimental results are presented1. © 2014 EURASIP.Show more Item Open Access Recovery of sparse perturbations in Least Squares problems(IEEE, 2011) Pilanci, M.; Arıkan, OrhanShow more We show that the exact recovery of sparse perturbations on the coefficient matrix in overdetermined Least Squares problems is possible for a large class of perturbation structures. The well established theory of Compressed Sensing enables us to prove that if the perturbation structure is sufficiently incoherent, then exact or stable recovery can be achieved using linear programming. We derive sufficiency conditions for both exact and stable recovery using known results of ℓ 0/ℓ 1 equivalence. However the problem turns out to be more complicated than the usual setting used in various sparse reconstruction problems. We propose and solve an optimization criterion and its convex relaxation to recover the perturbation and the solution to the Least Squares problem simultaneously. Then we demonstrate with numerical examples that the proposed method is able to recover the perturbation and the unknown exactly with high probability. The performance of the proposed technique is compared in blind identification of sparse multipath channels. © 2011 IEEE.Show more Item Open Access Seyrek sinyallerin geri çatımına özyineli bir yaklaşım(IEEE, 2014-04) Teke, Oğuzhan; Arıkan, Orhan; Gürbüz, A. C.Show more Sıkıştırılmış Algılama (SA) kuramı, bilinen bir tabanda seyrek olan bir sinyalin az sayıda ölçüm ile nasıl geri çatılacağını inceler. Çoğu pratik sistemdeki ölçüm sinyallerinin sürekli bir parametre uzayında seyrek bir tanıma sahip olması, SA kuramı altında geliştirilmiş tekniklerin kullanılabilme olasılığını ortaya çıkarır. Ancak, SA tekniklerinin uygulanabilmesi için sürekli parametre uzayının ayrıklaştırılması gerekir. Bu ayrıklaştırma sonucunda da iyi bilinen ızgara-dışılık problemi ortaya çıkar. Izgara-dışılık problemini engellemek için bu çalışmada, parametre alanını degişken ve uyarlamalı bir şekilde ayrıklaştıran özyineli bir yaklaşım sunulmuştur. Önerilen yaklaşımın çok yakın şekilde konumlanmış hedefleri dahi yüksek hassasiyetle kestirebildiği benzetim çalışmalarıyla gösterilmiştir.Show more Item Open Access Sparsity order estimation for single snapshot compressed sensing(IEEE, 2015-11) Romer, F.; Lavrenko, A.; Del Galdo, G.; Hotz, T.; Arıkan, Orhan; Thoma, R. S.Show more In this paper we discuss the estimation of the spar-sity order for a Compressed Sensing scenario where only a single snapshot is available. We demonstrate that a specific design of the sensing matrix based on Khatri-Rao products enables us to transform this problem into the estimation of a matrix rank in the presence of additive noise. Thereby, we can apply existing model order selection algorithms to determine the sparsity order. The matrix is a rearranged version of the observation vector which can be constructed by concatenating a series of non-overlapping or overlapping blocks of the original observation vector. In both cases, a Khatri-Rao structured measurement matrix is required with the main difference that in the latter case, one of the factors must be a Vandermonde matrix. We discuss the choice of the parameters and show that an increasing amount of block overlap improves the sparsity order estimation but it increases the coherence of the sensing matrix. We also explain briefly that the proposed measurement matrix design introduces certain multilinear structures into the observations which enables us to apply tensor-based signal processing, e.g., for enhanced denoising or improved sparsity order estimation. © 2014 IEEE.Show more Item Open Access Sub-band equalization of modulated wideband converter for improved dynamic range performance(IEEE, 2017) Korucu, A. B.; Alp, Y. K.; Gök, Gökhan; Arıkan, OrhanShow more In this work, we propose a new method to improve the dynamic range performance of the Modulated Wideband Converter (MWC), which is multi-channel sampling system for digitizing wideband sparse signals below the Nyquist limit without loss of information by using compressive sensing techniques. MWC achieves high dynamic range assuming that subband frequency responses of the system are identical. However, in hardware implementations of MWC, the resulting sub-band frequency responses are not identical and dynamic range performance of the system drops significantly which makes it unusable in practical applications. Proposed method iteratively designs FIR filters for equalizing frequency responses of the all sub-bands. Obtained results from the extensive computer simulations of the MWC system show that proposed method improves the dynamic range performance of the MWC system significantly.Show more