Browsing by Subject "Orthogonal projection"
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Item Open Access Adaptive decision fusion based cooperative spectrum sensing for cognitive radio systems(IEEE, 2011) Töreyin, B. U.; Yarkan, S.; Qaraqe, K. A.; Çetin, A. EnisIn this paper, an online Adaptive Decision Fusion (ADF) framework is proposed for the central spectrum awareness engine of a spectrum sensor network in Cognitive Radio (CR) systems. Online learning approaches are powerful tools for problems where drifts in concepts take place. Cooperative spectrum sensing in cognitive radio networks is such a problem where channel characteristics and utilization patterns change frequently. The importance of this problem stems from the requirement that secondary users must adjust their frequency utilization strategies in such a way that the communication performance of the primary users would not be degraded by any means. In the proposed framework, sensing values from several sensor nodes are fused together by weighted linear combination at the central spectrum awareness engine. The weights are updated on-line according to an active fusion method based on performing orthogonal projections onto convex sets describing power reading values from each sensor. The proposed adaptive fusion strategy for cooperative spectrum sensing can operate independent from the channel type between the primary user and secondary users. Results of simulations and experiments for the proposed method conducted in laboratory are also presented. © 2011 IEEE.Item Open Access Deconvolution using projections onto the epigraph set of a convex cost function(IEEE, 2014) Tofighi, Mohammad; Bozkurt, Alican; Köse, K.; Çetin, A. EnisA 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.Item Open Access Denoising using projections onto the epigraph set of convex cost functions(IEEE, 2014) Tofighi, Mohammad; Köse, K.; Çetin, A. EnisA 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.1Item Open Access Projection-based wavelet denoising [lecture notes](Institute of Electrical and Electronics Engineers Inc., 2015) Çetin, A. Enis; Tofighi M.In this lecture note, we describe a wavelet domain denoising method consisting of making orthogonal projections of wavelet (subbands) signals of the noisy signal onto an upside down pyramid-shaped region in a multidimensional space. Each horizontal slice of the upside down pyramid is a diamond shaped region and it is called an -ball. The upside down pyramid is called the epigraph set of the -norm cost function. We show that the method leads to soft-thresholding as in standard wavelet denoising methods. Orthogonal projection operations automatically determine the soft-threshold values of the wavelet signals. © 2015 IEEE.Item Open Access Projections onto convex sets (POCS) based optimization by lifting(IEEE, 2013) Çetin, A. Enis; Bozkurt, Alican; Günay, Osman; Habiboglu, Yusuf Hakan; Köse, K.; Onaran, İbrahim; Tofighi, Mohammad; Sevimli, Rasim AkınA new optimization technique based on the projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in RN the corresponding set which is the epigraph of the cost function is also a convex set in RN+1. The iterative optimization approach starts with an arbitrary initial estimate in R N+1 and an orthogonal projection is performed onto one of the sets in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation, filtered variation, l1, and entropic cost functions. It is also experimentally observed that cost functions based on lp; p < 1 may be handled by using the supporting hyperplane concept. The new POCS based method can be used in image deblurring, restoration and compressive sensing problems. © 2013 IEEE.Item Open Access Projections onto the epigraph set of the filtered variation function based deconvolution algorithm(IEEE, 2017) Tofighi, M.; Çetin, A. EnisA new deconvolution algorithm based on orthogonal projections onto the hyperplanes and the epigraph set of a convex cost function is presented. In this algorithm, the convex sets corresponding to the cost function are defined by increasing the dimension of the minimization problem by one. The Filtered Variation (FV) function is used as the convex cost function in this algorithm. Since the FV cost function is a convex function in RN, then the corresponding epigraph set is also a convex set in the lifted set in RN+1. At each step of the iterative deconvolution algorithm, starting with an arbitrary initial estimate in RN+1, first the projections onto the hyperplanes are performed to obtain the first deconvolution estimate. Then an orthogonal projection is performed onto the epigraph set of the FV cost function, in order to regularize and denoise the deconvolution estimate, in a sequential manner. The algorithm converges to the deblurred image.