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2015 | OriginalPaper | Chapter

Gabor Analysis for Imaging

Authors : Ole Christensen, Hans G. Feichtinger, Stephan Paukner

Published in: Handbook of Mathematical Methods in Imaging

Publisher: Springer New York

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Excerpt

In contrast to classical Fourier analysis, time–frequency analysis is concerned with localized Fourier transforms. Gabor analysis is an important branch of time–frequency analysis. Although significantly different, it shares with the wavelet transform methods the ability to describe the smoothness of a given function in a location-dependent way. …

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Literature
1.
Ali, S.T., Antoine, J.-P., Murenzi, R., Vandergheynst, P.: Two-Dimensional Wavelets and Their Relatives. Cambridge University Press, Cambridge (2004)MATH
2.
Assaleh, K., Zeevi, Y., Gertner, I.: On the realization of Zak-Gabor representation of images. In: Proceedings of SPIE: Visual Communications and Image Processing’91, Boston, vol. 1606, pp. 532–552. SPIE (1991)
3.
Bastiaans, M.J.: Gabor’s expansion of a signal into Gaussian elementary signals. Proc. IEEE 68(4), 538–539 (1980)CrossRef
4.
Bastiaans, M.J.: A sampling theorem for the complex spectrogram and Gabor’s expansion of a signal in Gaussian elementary signals. Opt. Eng. 20(4), 594–598 (1981)CrossRef
5.
Bastiaans, M.J.: On the sliding-window representation in digital signal processing. IEEE Trans. Acoust. Speech Signal Process. 33(4), 868–873 (1985)CrossRef
6.
Bastiaans, M.J.: Application of the Wigner distribution function to partially coherent light. J. Opt. Soc. Am. 3(8), 1227–1238 (1986)CrossRef
7.
Bastiaans, M.J.: Gabor’s signal expansion in optics. In: Feichtinger, H.G., Strohmer, T. (eds.) Gabor Analysis and Algorithms: Theory and Applications. Applied and Numerical Harmonic Analysis, pp. 427–451. Birkhäuser, Boston (1998)CrossRef
8.
Bastiaans, M.J., van Leest, A.J.: From the rectangular to the quincunx Gabor lattice via fractional Fourier transformation. IEEE Signal Proc. Lett. 5(8), 203–205 (1998)CrossRef
9.
Bastiaans, M.J., van Leest, A.J.: Product forms in Gabor analysis for a quincunx-type sampling geometry. In: Veen, J. (ed.) Proceedings of the CSSP-98, ProRISC/IEEE Workshop on Circuits, Systems and Signal Processing, Mierlo, 26–17 Nov 1998. STW, Technology Foundation, Utrecht, pp. 23–26 (1998)
10.
11.
Ben Arie, J., Rao, K.R.: Nonorthogonal signal representation by Gaussians and Gabor functions. IEEE Trans Circuits-II 42(6), 402–413 (1995)MATH
12.
Ben Arie, J., Wang, Z.: Gabor kernels for affine-invariant object recognition. In: Feichtinger, H.G., Strohmer, T. (eds.) Gabor Analysis and Algorithms: Theory and Applications. Birkhauser, Boston (1998)
13.
Bölcskei, H., Feichtinger, H.G., Gröchenig, K., Hlawatsch, F.: Discrete-time multi-window Wilson expansions: pseudo frames, filter banks, and lapped transforms. In: Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Paris, pp. 525–528 (1996)
14.
Bölcskei, H., Gröchenig, K., Hlawatsch, F., Feichtinger, H.G.: Oversampled Wilson expansions. IEEE Signal Proc. Lett. 4(4), 106–108 (1997)CrossRef
15.
16.
Christensen, O.: An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston (2003)CrossRefMATH
17.
Christensen, O.: Frames and Bases: An Introductory Course. Applied and Numerical Harmonic Analysis. Birkhäuser, Basel (2008)CrossRef
18.
19.
Cristobal, G., Navarro, R.: Blind and adaptive image restoration in the framework of a multiscale Gabor representation. In: Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Philadelphia, pp. 306–309 (1994)
20.
Cristobal, G., Navarro, R.: Space and frequency variant image enhancement based on a Gabor representation. Pattern Recognit. Lett. 15(3), 273–277 (1994)CrossRefMATH
21.
22.
Daubechies, I.: Time-frequency localization operators: a geometric phase space approach. IEEE Trans. Inf. Theory 34(4), 605–612 (1988)CrossRefMATHMathSciNet
23.
Daubechies, I.: The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inf. Theory 36(5), 961–1005 (1990)CrossRefMATHMathSciNet
24.
25.
Daubechies, I., Jaffard, S., Journé, J.L.: A simple Wilson orthonormal basis with exponential decay. SIAM J. Math. Anal. 22, 554–573 (1991)CrossRefMATHMathSciNet
26.
Daubechies, I., Landau, H.J., Landau, Z.: Gabor time-frequency lattices and the Wexler-Raz identity. J. Fourier Anal. Appl. 1(4), 437–478 (1995)CrossRefMATHMathSciNet
27.
Daugman, J.G.: Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression. IEEE Trans. Acoust. Speech Signal Process. 36(7), 1169–1179 (1988)CrossRefMATH
28.
Dubiner, Z., Porat, M.: Position-Variant Filtering in the Position Frequency Space: Performance Analysis and Filter Design, pp. 1–34 (1997)
29.
Dufaux, F., Ebrahimi, T., Geurtz, A., Kunt, M.: Coding of digital TV by motion-compensated Gabor decomposition. In: Tescher, A.G. (ed.) Proceedings of SPIE: Applications of Digital Image Processing XIV, Image Compression, San Diego, 22 July 1991, vol. 1567, pp. 362–379. SPIE (1991)
30.
Dufaux, F., Ebrahimi, T., Kunt, M.: Massively parallel implementation for real-time Gabor decomposition. In: Tzou, K.-H., Koga, T. (eds.) Proceedings of SPIE: Proceedings of Visual Communications and Image Processing’91: Image Processing, Boston. Volume 1606 of VLSI Implementation and Hardware Architectures, pp. 851–864. SPIE (1991)CrossRef
31.
Dunn, D., Higgins, W.E.: Optimal Gabor filters for texture segmentation. IEEE Trans. Image Process. 4(7), 947–964 (1995)CrossRef
32.
Ebrahimi, T., Kunt, M.: Image compression by Gabor expansion. Opt. Eng. 30(7), 873–880 (1991)CrossRef
33.
Ebrahimi, T., Reed, T.R., Kunt, M.: Video coding using a pyramidal Gabor expansion. In: Proceedings of SPIE: Visual Communications and Image Processing’90, Lausanne, vol. 1360, pp. 489–502. SPIE (1990)
34.
Feichtinger, H.G.: Modulation spaces: looking back and ahead. Sampl. Theory Signal Image Process. 5(2), 109–140 (2006)MATHMathSciNet
35.
Feichtinger, H.G., Gröchenig, K.: Banach spaces related to integrable group representations and their atomic decompositions, I. J. Funct. Anal. 86, 307–340 (1989)CrossRefMATH
36.
Feichtinger, H.G., Gröchenig, K.: Theory and practice of irregular sampling. In: Benedetto, J., Frazier, M. (eds.) Wavelets: Mathematics and Applications. Studies in Advanced Mathematics, pp. 305–363. CRC, Boca Raton (1994)
37.
38.
Feichtinger, H.G., Kaiblinger, N.: 2D-Gabor analysis based on 1D algorithms. In: Proceedings of the OEAGM-97, Hallstatt (1997)
39.
Feichtinger, H.G., Kozek, W.: Quantization of TF lattice-invariant operators on elementary LCA groups. In: Feichtinger, H.G., Strohmer, T. (eds.) Gabor Analysis and Algorithms. Theory and Applications. Applied and Numerical Harmonic Analysis, pp. 233–266, 452–488. Birkhäuser, Boston (1998)
40.
Feichtinger, H.G., Kozek, W., Luef, F.: Gabor analysis over finite Abelian groups. Appl. Comput. Harmonic Anal. 26, 230–248 (2009)CrossRefMATHMathSciNet
41.
Feichtinger, H.G., Kozek, W., Prinz, P., Strohmer, T.: On multidimensional non-separable Gabor expansions. In: Proceedings of SPIE: Wavelet Applications in Signal and Image Processing IV, Denver (1996)
42.
Feichtinger, H.G., Luef, F., Werther, T.: A guided tour from linear algebra to the foundations of Gabor analysis. In: Gabor and Wavelet Frames. Volume 10 of Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, pp. 1–49. World Scientific, Hackensack (2007)CrossRef
43.
Feichtinger, H.G., Strohmer, T., Christensen, O.: A group theoretical approach to Gabor analysis. Opt. Eng. 34, 1697–1704 (1995)CrossRef
44.
Folland, G.B.: Harmonic Analysis in Phase Space. Princeton University Press, Princeton (1989)MATH
45.
Gabor, D.: Theory Commun. J. IEE 93(26), 429–457 (1946)
46.
Gertner, I., Zeevi, Y.Y.: Image representation with position-frequency localization. In: International Conference on Acoustics, Speech, and Signal Processing (ICASSP-91), Toronto, vol. 4, pp. 2353–2356 (1991)
47.
Golub, G., van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)MATH
48.
Grafakos, L., Sansing, C.: Gabor frames and directional time frequency analysis. Appl. Comput. Harmonic Anal. 25(1), 47–67 (2008)CrossRefMATHMathSciNet
49.
Grigorescu, S., Petkov, N., Kruizinga, P.: Comparison of texture features based on Gabor filters. IEEE Trans. Image Process. 11(10), 1160–1167 (2002)CrossRefMathSciNet
50.
Gröchenig, K.: Aspects of Gabor analysis on locally compact Abelian groups. In: Feichtinger, H.G., Strohmer, T. (eds.) Gabor Analysis and Algorithms: Theory and Applications, pp. 211–231. Birkhäuser, Boston (1998)CrossRef
51.
Gröchenig, K.: Foundations of Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston (2001)CrossRefMATH
52.
Hoffmann, U., Naruniec, J., Yazdani, A., Ebrahimi, T.: Face detection using discrete Gabor jets and a probabilistic model of colored image patches. In: Filipe, J., Obaidat, M.S. (eds.) E-Business and Telecommunications (ICETE 2008), Porto, 26–29 July 2008. Revised Selected Papers, Volume 48 of Communications in Computer and Information Science, pp. 331–344 (2008)
53.
54.
55.
Janssen, A.J.E.M.: From continuous to discrete Weyl-Heisenberg frames through sampling. J. Fourier Anal. Appl. 3(5), 583–596 (1997)CrossRefMATHMathSciNet
56.
Kutyniok, G., Strohmer, T.: Wilson bases for general time-frequency lattices. SIAM J. Math. Anal. 37(3), 685–711 (electronic) (2005)CrossRefMATHMathSciNet
57.
Lee, T.S.: Image representation using 2D Gabor wavelets. IEEE Trans. Pattern Anal. Mach. Intell. 18(10), 959–971 (1996)CrossRef
58.
59.
Lu, Y., Morris, J.: Fast computation of Gabor functions. IEEE Signal Process. Lett. 3(3), 75–78 (1996)CrossRef
60.
Malvar, H.S.: Lapped transforms for efficient transform/subband coding. IEEE Trans. Acoust. Speech Signal Process. 38(6), 969–978 (1990)CrossRef
61.
Navarro, R., Portilla, J., Tabernero, A.: Duality between oveatization and multiscale local spectrum estimation. In: Rogowitz, B.E., Pappas, T.N. (eds.) Proceedings of SPIE: Human Vision and Electronic Imaging III, San Jose, 26 Jan 1998, vol. 3299, pp. 306–317. SPIE, Bellingham (1998)
62.
Nestares, O., Navarro, R., Portilla, J., Tabernero, A.: Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions. J. Electron. Imaging 7(1), 166–173 (1998)CrossRef
63.
Paukner, S.: Foundations of Gabor analysis for image processing. Master’s thesis, University of Vienna (2007)
64.
Porat, M., Zeevi, Y.Y.: The generalized Gabor scheme of image representation in biological and machine vision. IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 452–468 (1988)CrossRefMATH
65.
Porat, M., Zeevi, Y.Y.: Gram-Gabor approach to optimal image representation. In: Kunt, M. (ed.) Proceedings of SPIE: Visual Communications and Image Processing’90: Fifth in a Series, Lausanne, vol. 1360, pp. 1474–1478. SPIE (1990)CrossRef
66.
Prinz, P.: Calculating the dual Gabor window for general sampling sets. IEEE Trans. Signal Process. 44(8), 2078–2082 (1996)CrossRef
67.
Redding, N., Newsam, G.: Efficient calculation of finite Gabor transforms. IEEE Trans. Signal Process. 44(2), 190–200 (1996)CrossRef
68.
Redondo, R., Sroubek, F., Fischer, S., Cristobal, G.: Multifocus image fusion using the log-Gabor transform and a Multisize Windows technique. Inf. Fusion 10(2), 163–171 (2009)CrossRef
69.
70.
Shen, L., Bai, L., Fairhurst, M.: Gabor wavelets and general discriminant analysis for face identification and verification. Image Vis. Comput. 25(5), 553–563 (2007)CrossRef
71.
Søndergaard, P.L.: Finite discrete Gabor analysis. PhD thesis, Technical University of Denmark (2007)
72.
Strohmer, T.: Numerical algorithms for discrete Gabor expansions. In: Feichtinger, H.G., Strohmer, T. (eds.) Gabor Analysis and Algorithms: Theory and Applications, pp. 267–294. Birkhäuser, Boston (1997)
73.
Subbanna, N.K., Zeevi, Y.Y.: Image representation using noncanonical discrete multi-window Gabor frames. In: IET International Conference on Visual Information Engineering (VIE 2006), Bangalore, pp. 482–487 (2006)CrossRef
74.
Urieli, S., Porat, M., Cohen, N.: Optimal reconstruction of images from localized phase. IEEE Trans. Image Process. 7(6), 838–853 (1998)CrossRefMATHMathSciNet
75.
van Leest, A.J., Bastiaans, M.J.: Gabor’s signal expansion and the Gabor transform on a non-separable time-frequency lattice. J. Frankl. Inst. 337(4), 291–301 (2000)CrossRefMATH
76.
Vargas, A., Campos, J., Navarro, R.: An application of the Gabor multiscale decomposition of an image to pattern recognition. In: Proceedings of SPIE: Visual Communications and Image Processing’96, Orlando, vol. 2730, pp. 622–625. SPIE (1996)
77.
Weldon, T., Higgins, W., Dunn, D.: Efficient Gabor filter design for texture segmentation. Pattern Recognit. 29(12), 2005–2015 (1996)CrossRef
78.
Werner, D.: Funktionalanalysis. (Functional Analysis) 2., Überarb. Au. Springer, Berlin (1997)
79.
Wojdyllo, P.: Modified Wilson orthonormal bases. Sampl. Theory Signal Image Process. 6(2), 223–235 (2007)MATHMathSciNet
80.
Wojdyllo, P.: Characterization of Wilson systems for general lattices. Int. J. Wavelets Multiresolut. Inf. Process. 6(2), 305–314 (2008)CrossRefMATHMathSciNet
81.
Wojtaszczyk, P.: Stability and instance optimality for Gaussian measurements in compressed sensing. Found. Comput. Math. 10, 1–13 (2010)CrossRefMATHMathSciNet
82.
Yang, J., Liu, L., Jiang, T., Fan, Y.: A modified Gabor filter design method for fingerprint image enhancement. Pattern Recognit. Lett. 24(12), 1805–1817 (2003)CrossRef
83.
Zeevi, Y.Y.: Multiwindow Gabor-type representations and signal representation by partial information. In: Byrnes, J.S. (ed.) Twentieth Century Harmonic Analysis – A Celebration Proceedings of the NATO Advanced Study Institute, II, Ciocco, 2–15 July 2000. Volume 33 of NATO Science Series II, Mathematics, Physics, and Chemistry, pp. 173–199. Kluwer, Dordrecht (2001)
84.
Zeevi, Y.Y., Zibulski, M., Porat, M.: Multi-window Gabor schemes in signal and image representations. In: Feichtinger, H.G., Strohmer, T. (eds.) Gabor Analysis and Algorithms: Theory and Applications. Applied and Numerical Harmonic Analysis, pp. 381–407. Birkhäuser, Boston (1998)CrossRef
85.
Zibulski, M., Zeevi, Y.Y.: Matrix algebra approach to Gabortype image representation. In: Haskell, B.G., Hang, H.-M. (eds.) Proceedings of SPIE: Visual Communications and Image Processing’93, Wavelet, Cambridge, 08 Nov 1993, vol. 2094, pp. 1010–1020. SPIE (1993)
86.
Zibulski, M., Zeevi, Y.Y.: Frame analysis of the discrete Gaborscheme. IEEE Trans. Signal Process. 42(4), 942–945 (1994)CrossRef
87.
Zibulski, M., Zeevi, Y.Y.: Analysis of multiwindow Gabor-type schemes by frame methods. Appl. Comput. Harmonic Anal. 4(2), 188–221 (1997)CrossRefMATHMathSciNet
88.
Zibulski, M., Zeevi, Y.Y.: Discrete multiwindow Gabor-type transforms. IEEE Trans. Signal Process. 45(6), 1428–1442 (1997)CrossRefMATH
89.
Zibulski, M., Zeevi, Y.Y.: The generalized Gabor scheme and its application in signal and image representation. In: Signal and Image Representation in Combined Spaces. Volume 7 of Wavelet Analysis and Its Applications, pp. 121–164. Academic, San Diego (1998)
Metadata
Title
Gabor Analysis for Imaging
Authors
Ole Christensen
Hans G. Feichtinger
Stephan Paukner
Copyright Year
2015
Publisher
Springer New York
Book
Handbook of Mathematical Methods in Imaging

Print ISBN: 978-1-4939-0789-2

Electronic ISBN: 978-1-4939-0790-8

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-1-4939-0790-8_54

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