Image processing by alternate dual Gabor frames

Document Type: Research Paper

Authors

1 Department of Mathematics and Computer Sciences‎, ‎Hakim Sabzevari University‎, ‎Sabzevar‎, ‎Iran.

2 Department of Mathematics‎, ‎Shahrood University of‎ ‎Technology‎, ‎Shahrood‎, ‎Iran.

Abstract

‎We present an application of the dual Gabor frames to image‎ ‎processing‎. ‎Our algorithm is based on finding some dual Gabor‎ ‎frame generators which reconstructs accurately the elements of the‎ ‎underlying Hilbert space‎. ‎The advantages of these duals‎ ‎constructed by a polynomial of Gabor frame generators are compared‎ ‎with their canonical dual‎.

Keywords

Main Subjects


A. Arefijamaal and E. Zekaee, Signal processing by alternate dual Gabor frames, Appl.  Comput. Harmon. Anal. 35 (2013) 535--540.

P. Balazs, H. G. Feichtinger, M. Hampejs and G. Kracher, Double preconditioning for Gabor frames, IEEE Trans. Signal Process. 35 (2006), no. 12, 4597--4610.

J. Benedetto, A. Powell and O. Yilmaz, Sigma-Delta quantization and finite frames, IEEE Trans. Inform. Theory 52 (2006) 1990--2005.

P. G. Casazza, G. Kutyniok and M. C. Lammers, Duality principles in frame theory, J. Fourier Anal. Appl. 10 (2004), no. 4, 383--408.

O. Christensen, Frames and Bases, An Introductory Course, Birkhauser, Boston, 2008.

O. Christensen, Pairs of dual Gabor frames with compact support and desired frequency localization, Appl. Comput. Harmon. Anal. 20 (2006) 403--410.

O. Christensen, H. G. Feichtinger and S. Paukner, Gabor Analysis for Imaging, Vol. 3, Springer, Berlin, 2011.

O. Christensen and R. Y. Kim, On dual Gabor frame pairs generated by polynomials, J. Fourier Anal. Appl. 16 (2010) 11--16.

I. Daubechies, H. J. Landau and Z. Landau, Gabor time-frequency lattices and the Wexler-Raz identity, J. Fourier Anal. Appl. 1 (1995), no. 4, 437--478.

H. G. Feichtinger and T. Strohmer, Gabor Analysis and Algorithms: Theory and Applications, Birkhauser, Boston, 1997.

G. B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, Boca Raton, 1995.

M. Gaianu and D. M. Onchis, Face and marker detection using Gabor frames on GPUs, Signal Processing 90 (2013) 90--93.

A. Ghaani Farashahi, Continuous partial Gabor transform for semi-direct product of locally compact groups, Bull. Malays. Math. Sci. Soc. 38 (2015), no. 2, 779--803.

A. Ghaani Farashahi and R. Kamyabi-Gol, Continuous Gabor transform for a class of non-abelian groups, Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 4, 683--701.

K. Grochenig, Foundations of Time-Frequency Analysis, Birkhauser, Boston, 2001.

R. W. Heath and A. J. Paulraj, Linear dispersion codes for MIMO systems based on frame theory, IEEE Trans. Signal Process. 50 (2002) 2429--2441.

A. J. E. M. Janssen, The duality condition for Weyl-Heisenberg frames, in: H. G. Feichtinger and T. Strohmer (eds.), Gabor Analysis: Theory and Applications, pp. 33--84, Birkhauser, Boston, 1998.

A. Khosravi and M. S. Asgari, Frames and bases in tensor product of Hilbert spaces, Intern. Math. Journal 4 (2003), no. 6, 527--537.

G. E. Pfander, Gabor frames in finite dimensions, in: P. G. Casazza and G. Kutyniok (eds.) Finite Frames: Theory and Applications, pp. 193--240, Birkhauser, Boston, 2013.

S. Qiu, Generalized dual Gabor atoms and best approximations by Gabor family, Signal Processing 49 (1996) 167--186.

A. Ron and Z. Shen, Weyl-Heisenberg frames and Riesz bases in L2(Rd), Duke Math. J. 89 (1997), no. 2, 237--282.

J. Wexler and S. Raz, Discrete Gabor expansions, Signal Processing 21 (1990) 207--221.


Volume 42, Issue 6
November and December 2016
Pages 1305-1314
  • Receive Date: 04 April 2015
  • Revise Date: 17 August 2015
  • Accept Date: 19 August 2015