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Author

M.A. Kutay

Other affiliations: Georgia Institute of Technology
Bio: M.A. Kutay is an academic researcher from Bilkent University. The author has contributed to research in topics: Fractional Fourier transform & Discrete-time Fourier transform. The author has an hindex of 11, co-authored 13 publications receiving 2203 citations. Previous affiliations of M.A. Kutay include Georgia Institute of Technology.

Papers
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Journal ArticleDOI
TL;DR: An algorithm for efficient and accurate computation of the fractional Fourier transform for signals with time-bandwidth product N, which computes the fractionsal transform in O(NlogN) time.
Abstract: 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.

1,034 citations

Journal ArticleDOI
TL;DR: 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, and is exactly unitary, index additive, and reduces to the D FT for unit order.
Abstract: 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.

604 citations

Journal ArticleDOI
TL;DR: An adaptive smoothing technique for speckle suppression in medical B-scan ultrasonic imaging is presented and the results show that the filter effectively reduces the Speckle while preserving the resolvable details.
Abstract: 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. >

211 citations

Proceedings ArticleDOI
15 Mar 1999
TL;DR: This definition is based on a particular set of eigenvectors of the DFT which constitutes the discrete counterpart of the set of Hermite-Gaussian functions and supports confidence that it will be accepted as the definitive definition of this transform.
Abstract: We propose and consolidate a definition of the discrete fractional Fourier transform which generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform (FRT) generalizes the continuous ordinary Fourier Transform. This definition is based on a particular set of eigenvectors of the DFT which constitutes the discrete counterpart of the set of Hermite-Gaussian functions. The fact that this definition satisfies all the desirable properties expected of the discrete FRT, supports our confidence that it will be accepted as the definitive definition of this transform.

210 citations

Proceedings ArticleDOI
09 May 1995
TL;DR: The optimal fractional Fourier domain filter is derived that minimizes the MSE for given non-stationary signal and noise statistics, and time-varying distortion kernel.
Abstract: The ordinary Fourier transform is suited best for analysis and processing of time-invariant signals and systems. When we are dealing with time-varying signals and systems, filtering in fractional Fourier domains might allow us to estimate signals with smaller minimum mean square error (MSE). We derive the optimal fractional Fourier domain filter that minimizes the MSE for given non-stationary signal and noise statistics, and time-varying distortion kernel. We present an example for which the MSE is reduced by a factor of 50 as a result of filtering in the fractional Fourier domain, as compared to filtering in the conventional Fourier or time domains. We also discuss how the fractional Fourier transformation can be computed in O(N log N) time, so that the improvement in performance is achieved with little or no increase in computational complexity.

130 citations


Cited by
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Journal ArticleDOI
TL;DR: This paper reviews ultrasound segmentation methods, in a broad sense, focusing on techniques developed for medical B-mode ultrasound images, and presents a classification of methodology in terms of use of prior information.
Abstract: This paper reviews ultrasound segmentation methods, in a broad sense, focusing on techniques developed for medical B-mode ultrasound images. First, we present a review of articles by clinical application to highlight the approaches that have been investigated and degree of validation that has been done in different clinical domains. Then, we present a classification of methodology in terms of use of prior information. We conclude by selecting ten papers which have presented original ideas that have demonstrated particular clinical usefulness or potential specific to the ultrasound segmentation problem

1,150 citations

Journal ArticleDOI
TL;DR: An algorithm for efficient and accurate computation of the fractional Fourier transform for signals with time-bandwidth product N, which computes the fractionsal transform in O(NlogN) time.
Abstract: 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.

1,034 citations

Journal ArticleDOI
TL;DR: Time-frequency domain signal processing using energy concentration as a feature is a very powerful tool and has been utilized in numerous applications and the expectation is that further research and applications of these algorithms will flourish in the near future.

646 citations

Journal ArticleDOI
TL;DR: 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, and is exactly unitary, index additive, and reduces to the D FT for unit order.
Abstract: 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.

604 citations

Journal ArticleDOI
TL;DR: Results on real images demonstrate that the proposed adaptation of the nonlocal (NL)-means filter for speckle reduction in ultrasound (US) images is able to preserve accurately edges and structural details of the image.
Abstract: In image processing, restoration is expected to improve the qualitative inspection of the image and the performance of quantitative image analysis techniques. In this paper, an adaptation of the nonlocal (NL)-means filter is proposed for speckle reduction in ultrasound (US) images. Originally developed for additive white Gaussian noise, we propose to use a Bayesian framework to derive a NL-means filter adapted to a relevant ultrasound noise model. Quantitative results on synthetic data show the performances of the proposed method compared to well-established and state-of-the-art methods. Results on real images demonstrate that the proposed method is able to preserve accurately edges and structural details of the image.

547 citations