Browsing by Author "Deprem, Zeynel"

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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
Sparsity and convex programming in time-frequency processing
(2014-12) Deprem, Zeynel
In this thesis sparsity and convex programming-based methods for timefrequency (TF) processing are developed. The proposed methods aim to obtain high resolution and cross-term free TF representations using sparsity and lifted projections. A crucial aspect of Time-Frequency (TF) analysis is the identification of separate components in a multi component signal. Wigner-Ville distribution is the classical tool for representing such signals but suffers from cross-terms. Other methods that are members of Cohen’s class distributions also aim to remove the cross terms by masking the Ambiguity Function (AF) but they result in reduced resolution. Most practical signals with time-varying frequency content are in the form of weighted trajectories on the TF plane and many others are sparse in nature. Therefore the problem can be cast as TF distribution reconstruction using a subset of AF domain coefficients and sparsity assumption in TF domain. Sparsity can be achieved by constraining or minimizing the l1 norm. Projections Onto Convex Sets (POCS) based l1 minimization approach is proposed to obtain a high resolution, cross-term free TF distribution. Several AF domain constraint sets are defined for TF reconstruction. Epigraph set of l1 norm, real part of AF and phase of AF are used during the iterative estimation process. A new kernel estimation method based on a single projection onto the epigraph set of l1 ball in TF domain is also proposed. The kernel based method obtains the TF representation in a faster way than the other optimization based methods. Component estimation from a multicomponent time-varying signal is considered using TF distribution and parametric maximum likelihood (ML) estimation. The initial parameters are obtained via time-frequency techniques. A method, which iterates amplitude and phase parameters separately, is proposed. The method significantly reduces the computational complexity and convergence time.
Open Access
Zaman-frekans dağılımı için çekirdek kestirimi
(IEEE, 2015-05) Deprem, Zeynel; Çetin, A. Enis
Bu dokümanda çözünürlüğü yüksek ve çapraz terim içermeyen Cohen sınıfı bir Zaman-frekans (ZF) dağılımının, çekirdek kestirim yöntemi ile elde edilmesi tanıtılmaktadır. Çekirdek kestirimi, başlangıç taslak bir zaman-frekans dağılımının l1 normuna ait epigraf kümesi üzerine izdüşümü ile elde edilmektedir. Kestirilen çekirdek, sinyalin belirsizlik (Ambiguity) düzlemindeki hizalanması ile uyumlu ve çapraz terimleri içermeyecek bir filtreleme sağlamaktadır.