Signal recovery from partial fractional Fourier domain information and its applications
Signal recovery from partial fractional Fourier domain information and its applications
- Author(s): H.E. Guven ; H.M. Ozaktas ; A.E. Cetin ; B. Barshan
- DOI: 10.1049/iet-spr:20070017
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- Author(s): H.E. Guven 1 ; H.M. Ozaktas 2 ; A.E. Cetin 2 ; B. Barshan 2
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View affiliations
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Affiliations:
1: CenSSIS Headquarters, Northeastern University, Boston, USA
2: Department of Electrical and Electronics Engineering, Bilkent University, Ankara, Turkey
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Affiliations:
1: CenSSIS Headquarters, Northeastern University, Boston, USA
- Source:
Volume 2, Issue 1,
March 2008,
p.
15 – 25
DOI: 10.1049/iet-spr:20070017 , Print ISSN 1751-9675, Online ISSN 1751-9683
The problem of recovering signals from partial fractional Fourier transform information arises in wave propagation problems where the measured information is partial, spread over several observation planes, or not of sufficient spatial resolution or accuracy. This problem can be solved with the method of projections onto convex sets, with the convergence of the iterative algorithm being assured. Several prototypical application scenarios and simulation examples are presented.
Inspec keywords: iterative methods; Fourier transforms; signal processing
Other keywords:
Subjects: Interpolation and function approximation (numerical analysis); Signal processing theory; Integral transforms in numerical analysis; Integral transforms in numerical analysis; Interpolation and function approximation (numerical analysis); Signal processing and detection
References
-
-
1)
- P.L. Combettes . The foundations of set theoretic estimation. Proc. IEEE , 2 , 182 - 208
-
2)
- F. Akyildiz , W. Su , Y. Sankara subramaniam . A survey on sensor networks. IEEE Trans. Commun. Mag. , 8 , 102 - 114
-
3)
- B. Barshan , M.A. Kutay , H.M. Ozaktas . Optimal filtering with linear canonical transformations. Opt. Commun. , 32 - 36
-
4)
- A.E. Cetin , H. Özaktaş , H.M. Ozaktas . Resolution enhancement of low resolution wavefields with POCS algorithm. Electron. Lett. , 1808 - 1810
-
5)
- H.M. Ozaktas , O. Aytür . Fractional Fourier domains. Signal Process. , 119 - 124
-
6)
- M.I. Sezan , H. Stark . Image restoration by the method of convex projections, part-2: Applications and numerical results. IEEE Trans. Med. Imaging , 2 , 95 - 101
-
7)
- D. Mendlovic , H.M. Ozaktas . Fractional Fourier transforms and their optical implementation: I. J. Opt. Soc. Am. A , 1875 - 1881
-
8)
- Guest editorial on Swarm robotics. Auton. Robots , 111 - 113
-
9)
- H. Ozaktas , O. Arikan , M.A. Kutay , G. Bozdagi . Digital computation of the fractional Fourier transform. IEEE Trans. Signal Process. , 9 , 2141 - 2150
-
10)
- Candan Ç: ‘Discrete fractional Fourier transform matrix generator’ MATLAB program, 1998. Available at http://www.ee.bilkent.edu.tr/_haldun/dFRT.m.
-
11)
- S.S. Iyengar , R.R. Brooks . (2004) Distributed sensor networks.
-
12)
- Yetik, İ.Ş., Kutay, M.A., Özaktaş, H.: `Continuous and discrete fractional Fourier domain decomposition', Proc. 2000 IEEE Int. Conf. Acoust, Speech, and Signal Processing, 2000, I, p. 93–96.
-
13)
- A.E. Cetin , R. Ansari . A convolution based framework for signal recovery. J. Opt. Soc. Am. A , 1193 - 1200
-
14)
- D.C. Youla , H. Webb . Image restoration by the method of convex projections, part-1: Theory. IEEE Trans. Med. Imaging , 2 , 81 - 94
-
15)
- A.E. Cetin , O.N. Gerek , Y. Yardimci . Equiripple FIR filter design by the FFT algorithm. IEEE Signal Process. Mag. , 60 - 64
-
16)
- H. Stark . (1987) Image recovery – theory and application.
-
17)
- Cetin, A.E., Özaktaş, H., Ozaktas, H.M.: `Signal recovery from partial fractional Fourier transform information', Proc. 1st Int. Symp. Control, Communications and Signal Processing (ISCCSP 2004), March 2004, p. 217–220.
-
18)
- R. Tao , B. Deng , Y. Wang . Research progress of the fractional Fourier transform in signal processing. Sci. China (Ser. F, Inf. Sci.) , 1 - 25
-
19)
- M.F. Erden , M.A. Kutay , H.M. Ozaktas . Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration. IEEE Trans. Signal Process. , 1458 - 1462
-
20)
- C. Candan , M.A. Kutay , H.M. Ozaktas . The discrete fractional Fourier transform. IEEE Trans. Signal Process. , 5 , 1329 - 1337
-
21)
- H.M. Ozaktas , D. Mendlovic . Fractional Fourier transforms and their optical implementation: II. J. Opt. Soc. Am. A , 2522 - 2531
-
22)
- Swarm robotics: state-of the-art survey. Lect. Notes Comput. Sci.
-
23)
- L.B. Almeida . The fractional Fourier transform and time-frequency representations. IEEE Trans. Signal Process. , 3084 - 3091
-
24)
- İ.Ş. Yetik , H.M. Ozaktas , B. Barshan . Perspective projections in the space-frequency plane and fractional Fourier transforms. J. Opt. Soc. Am. A , 2382 - 2390
-
25)
- H.M. Ozaktas , B. Barshan , D. Mendlovic . Convolution, filtering and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms. J. Opt. Soc. Am. A , 547 - 559
-
26)
- H.M. Ozaktas , D. Mendlovic . Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators. Opt. Lett. , 1678 - 1680
-
27)
- H.J. Trussell , M.R. Civanlar . The feasible solution in signal restoration. IEEE Trans. Acoust. Speech Signal Process , 201 - 212
-
28)
- P.L. Combettes . (1996) The convex feasibility problem in image recovery’, Advances in Imaging and Electron Physics.
-
29)
- L. Barker , Ç. Candan , T. Hakioğlu . The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform. J. Phys. A , 2209 - 2222
-
30)
- M.A. Kutay , H. Özaktaş , H.M. Ozaktas . The fractional Fourier domain decomposition. Signal Process. , 105 - 109
-
31)
- M.A. Kutay , H.M. Ozaktas . Optimal image restoration with the fractional Fourier transform. J. Opt. Soc. Am. A , 825 - 833
-
32)
- B. Barshan , B. Ayrulu . Fractional Fourier transform preprocessing for neural networks and its application to object recognition. Neural Netw. , 131 - 140
-
33)
- H.M. Ozaktas , D. Mendlovic . Fractional Fourier optics. J. Opt. Soc. Am. A , 743 - 751
-
34)
- H.M. Ozaktas , Z. Zalevsky , M.A. Kutay . (2001) The fractional Fourier transform with applications in optics and signal processing.
-
35)
- A.E. Cetin , R. Ansari . Signal recovery from wavelet transform maxima. IEEE Trans. Signal Process. , 194 - 196
-
36)
- M.F. Erden , H.M. Ozaktas , D. Mendlovic . Synthesis of mutual intensity distributions using the fractional Fourier transform. Opt. Commun. , 288 - 301
-
1)