Browsing by Author "Kutay, M. A."
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Item Open Access An adaptive speckle suppression filter for medical ultrasound imaging(Institute of Electrical and Electronics Engineers, 1995-06) Karaman, M.; Kutay, M. A.; Bozdagi, G.An adaptive smoothing technique for speckle suppression in medical B-scan ultrasonic imaging is presented. The technique is based on filtering with appropriately shaped and sized local kernels. For each image pixel, a filtering kernel, which fits to the local homogeneous region containing the processed pixel, is obtained through a local statistics based region growing technique. The performance of the proposed filter has been tested on the phantom and tissue images. The results show that the filter effectively reduces the speckle while preserving the resolvable details. The simulation results are presented in a comparative way with two existing speckle suppression methods.Item Open Access Continuous and discrete fractional fourier domain decomposition(IEEE, 2000) Yetik, İ. Şamil; Kutay, M. A.; Özaktaş, H.; Özaktaş, Haldun M.We introduce the fractional Fourier domain decomposition for continuous and discrete signals and systems. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation of space-variant linear systems.Item Open Access Digital computation of linear canonical transforms(Institute of Electrical and Electronics Engineers, 2008) Koç A.; Özaktaş, Haldun M.; Candan, C.; Kutay, M. A.We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation, and scaling operations. The second is based on decomposition of the LCT into a fractional Fourier transform followed by scaling and chirp multiplication. Both algorithms take ∼ N log N time, where N is the time-bandwidth product of the signals. The only essential deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus, the algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy.Item Open Access Digital computation of the fractional Fourier transform(Institute of Electrical and Electronics Engineers, 1996-09) Özaktaş, Haldun M.; Arıkan, Orhan; Kutay, M. A.; Bozdağı, G.An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also discussed.Item Open Access The discrete fractional Fourier transform(IEEE, 2000-05) Candan, C.; Kutay, M. A.; Özaktaş, Haldun M.We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of Hermite–Gaussian functions. The definition is exactly unitary, index additive, and reduces to the DFT for unit order. The fact that this definition satisfies all the desirable properties expected of the discrete fractional Fourier transform supports our confidence that it will be accepted as the definitive definition of this transform.Item Open Access The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform(Institute of Physics Publishing, 2000) Barker, L.; Candan, C.; Hakioğlu, T.; Kutay, M. A.; Özaktaş, Haldun M.Certain solutions to Harper's equation are discrete analogues of (and approximations to) the Hermite-Gaussian functions. They are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the time-evolution operator of the discrete harmonic oscillator.Item Open Access Effect of fractional Fourier transformation on time-frequency distributions belonging to the Cohen class(Institute of Electrical and Electronics Engineers, 1996-02) Özaktaş, Haldun M.; Erkaya, N.; Kutay, M. A.We consider the Cohen (1989) class of time-frequency distributions, which can be obtained from the Wigner distribution by convolving it with a kernel characterizing that distribution. We show that the time-frequency distribution of the fractional Fourier transform of a function is a rotated version of the distribution of the original function, if the kernel is rotationally symmetric. Thus, the fractional Fourier transform corresponds to rotation of a relatively large class of time-frequency representations (phase-space representations), confirming the important role this transform plays in the study of such representations.Item Open Access Efficient computation of quadratic-phase integrals in optics(Optical Society of America, 2006) Özaktaş, H. M.; Koç, A.; Sarı, I.; Kutay, M. A.Received June 29, 2005; revised manuscript received August 22, 2005; accepted September 12, 2005 We present a fast N log N time algorithm for computing quadratic-phase integrals. This three-parameter class of integrals models propagation in free space in the Fresnel approximation, passage through thin lenses, and propagation in quadratic graded-index media as well as any combination of any number of these and is therefore of importance in optics. By carefully managing the sampling rate, one need not choose N much larger than the space–bandwidth product of the signals, despite the highly oscillatory integral kernel. The only deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus the algorithm computes quadratic-phase integrals with a performance similar to that of the fast-Fourier-transform algorithm in computing the Fourier transform, in terms of both speed and accuracy. © 2006 Optical Society of AmericaItem Open Access Fast algorithms for digital computation of linear canonical transforms(Springer, New York, 2016) Koç, A.; Oktem, F. S.; Özaktaş, Haldun M.; Kutay, M. A.; Healy, J. J.; Kutay, M. A.; Özaktaş, Haldun M.; Sheridan, J. T.Fast and accurate algorithms for digital computation of linear canonical transforms (LCTs) are discussed. Direct numerical integration takes O.N2/ time, where N is the number of samples. Designing fast and accurate algorithms that take O.N logN/ time is of importance for practical utilization of LCTs. There are several approaches to designing fast algorithms. One approach is to decompose an arbitrary LCT into blocks, all of which have fast implementations, thus obtaining an overall fast algorithm. Another approach is to define a discrete LCT (DLCT), based on which a fast LCT (FLCT) is derived to efficiently compute LCTs. This strategy is similar to that employed for the Fourier transform, where one defines the discrete Fourier transform (DFT), which is then computed with the fast Fourier transform (FFT). A third, hybrid approach involves a DLCT but employs a decomposition-based method to compute it. Algorithms for two-dimensional and complex parametered LCTs are also discussed.Item Open Access The fractional Fourier domain decomposition(Elsevier, 1999) Kutay, M. A.; Özaktaş, H.; Özaktaş, Haldun M.; Arıkan, OrhanWe introduce the fractional Fourier domain decomposition. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation of space-variant linear systems.Item Open Access The fractional fourier transform(IEEE, 2001) Özaktas, Haldun M.; Kutay, M. A.A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phase-space representations (time- or space-frequency representations) and the concept of fractional Fourier domains are discussed. An overview of applications which have so far received interest are given and some potential application areas remaining to be explored are noted.Item Open Access Fractional fourier transform(CRC Press, 2010) Özaktaş, Haldun M.; Kutay, M. A.; Candan, Ç.; Poularikas, A. D.Item Open Access The Fractional Fourier transform and harmonic oscillation(Springer, 2002) Kutay, M. A.; Özaktaş, Haldun M.The ath-order fractional Fourier transform is a generalization of the ordinary Fourier transform such that the zeroth-order fractional Fourier transform operation is equal to the identity operation and the first-order fractional Fourier transform is equal to the ordinary Fourier transform. This paper discusses the relationship of the fractional Fourier transform to harmonic oscillation; both correspond to rotation in phase space. Various important properties of the transform are discussed along with examples of common transforms. Some of the applications of the transform are briefly reviewed.Item Open Access The fractional fourier transform and its applications to image representation and beamforming(ASME, 2003-09) Yetik, I. Ş; Kutay, M. A.; Özaktaş, Haldun. M.The ath order fractional Fourier transform operator is the ath power of the ordinary Fourier transform operator. We provide a brief introduction to the fractional Fourier transform, discuss some of its more important properties, and concentrate on its applications to image representation and compression, and beamforming. We show that improved performance can be obtained by employing the fractional Fourier transform instead of the ordinary Fourier transform in these applications.Item Open Access Image representation and compression with the fractional Fourier transform(Elsevier, 2001-04-01) Yetik, İ. Ş.; Kutay, M. A.; Özaktaş, Haldun M.We discuss the application of fractional Fourier transform-based filtering configurations to image representation and compression. An image can be approximately represented (and stored or transmitted) as the coefficients of the minimum mean square filtering configuration approximating the image matrix. An order of magnitude compression is possible with moderate errors with the raw method. While inferior to commonly available compression algorithms, the results presented correspond to the basic method without any refinement or combination with other techniques, suggesting that the approach may hold promise for future development. Regardless of its practical usefulness, the fact that the information inherent in an image can be decomposed or factored into fractional Fourier domains is of considerable conceptual significance. The information contained in the image is distributed to the different domains in an unequal way, making some domains more dispensible than others in representing the image. (C) 2001 Published by Elsevier Science B.V.Item Open Access Improved acoustics signals discrimination using fractional Fourier transform based phase-space representations(Elsevier, 2001-04-01) Zalevsky, Z.; Mendlovic, D.; Kutay, M. A.; Özaktaş, Haldun M.; Solomon, J.In this communication we propose performing two-dimensional correlation operation between phase-space representations based on the fractional Fourier transform, instead of correlating the signals themselves. A numerical examples clearly indicates superior discrimination performance. (C) 2001 Published by Elsevier Science B.V.Item Open Access Linear algebraic theory of partial coherence: continuous fields and measures of partial coherence(Optical Society of America, 2016) Özaktaş, Haldun M.; Gulcu, T. C.; Kutay, M. A.This work presents a linear algebraic theory of partial coherence for optical fields of continuous variables. This approach facilitates use of linear algebraic techniques and makes it possible to precisely define the concepts of incoherence and coherence in a mathematical way. We have proposed five scalar measures for the degree of partial coherence. These measures are zero for incoherent fields, unity for fully coherent fields, and between zero and one for partially coherent fields. � 2016 Optical Society of America.Item Open Access Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence(OSA Publishing, 2002) Özaktaş, Haldun M.; Yuksel, S.; Kutay, M. A.A linear algebraic theory of partial coherence is presented that allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights but also allows us to employ the conceptual and algebraic tools of linear algebra in applications. We define several scalar measures of the degree of partial coherence of an optical field that are zero for full incoherence and unity for full coherence. The mathematical definitions are related to our physical understanding of the corresponding concepts by considering them in the context of Young’s experiment. © 2002 Optical Society of AmericaItem Open Access Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence(SPIE, 2003-08) Özaktaş, Haldun M.; Yüksel, S.; Kutay, M. A.We present a linear algebraic theory of partial coherence which allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights, but also allows us to employ the tools of linear algebra in applications. We define a scalar measure of the degree of partial coherence of an optical field which is zero for complete incoherence and unity for full coherence.Item Open Access Nonseperable two-dimensional fractional Fourier transform(Optical Society of America, 1998) Sahin, A.; Kutay, M. A.; Özaktaş, Haldun M.Previous generalizations of the fractional Fourier transform to two dimensions assumed separable kernels. We present a nonseparable definition for the two-dimensional fractional Fourier transform that includes the separable definition as a special case. Its digital and optical implementations are presented. The usefulness of the nonseparable transform is justified with an image-restoration example.