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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 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 Filtered Variation method for denoising and sparse signal processing(IEEE, 2012) Köse, Kıvanç; Cevher V.; Çetin, A. EnisShow more We propose a new framework, called Filtered Variation (FV), for denoising and sparse signal processing applications. These problems are inherently ill-posed. Hence, we provide regularization to overcome this challenge by using discrete time filters that are widely used in signal processing. We mathematically define the FV problem, and solve it using alternating projections in space and transform domains. We provide a globally convergent algorithm based on the projections onto convex sets approach. We apply to our algorithm to real denoising problems and compare it with the total variation recovery. © 2012 IEEE.Show more Item Open Access A new OMP technique for sparse recovery(IEEE, 2012) Teke, Oğuzhan; Gürbüz, A.C.; Arıkan, OrhanShow more Compressive Sensing (CS) theory details how a sparsely represented signal in a known basis can be reconstructed using less number of measurements. However in reality there is a mismatch between the assumed and the actual bases due to several reasons like discritization of the parameter space or model errors. Due to this mismatch, a sparse signal in the actual basis is definitely not sparse in the assumed basis and current sparse reconstruction algorithms suffer performance degradation. This paper presents a novel orthogonal matching pursuit algorithm that has a controlled perturbation mechanism on the basis vectors, decreasing the residual norm at each iteration. Superior performance of the proposed technique is shown in detailed simulations. © 2012 IEEE.Show more Item 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. EnisShow more 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.Show more Item Open Access Sıkıştırılmış algılama kullanarak Uzaklık-Doppler radar hedef tespiti(IEEE, 2014-04) Sevimli, R. Akın; Tofighi, Mohammad; Çetin, A. EnisShow more Sıkıştırılmış algılama(SA) fikri, az sayıda ölçümlerden seyrek bir sinyalin geri çatımını mümkün kılar. SA yaklaşımı bir çok farklı alanda uygulamalara sahiptir. Bu alanlardan birisi de radar sistemleridir. Bu makalede, radar belirsizlik fonksiyonu (Ambiguity Function) SA çatısı altında gürültüden arındırılmıştır. Bu amaç için dışbükey fonksiyonun epigraf kümesine izdüşüm tabanlı yeni bir gürültüden arındırma metodu geliştirilmiştir. Bu yaklaşım, diğer SA geri çatım algoritmalarıyla karşılaştırılmıştır. Deneysel sonuçlar sunulmuştur.Show more