Abstract
Fourier transform has been extensively used in signal processing to analyze stationary signals. A serious drawback of the Fourier transform is that it cannot reflect the time evolution of the frequency.
References
- 1.A. Grossman, J. Morlet, Decompositions of hardy functions into square integrable wavelets of constant shape. SIAM J Math Anal 15(4), 75–79 (1984)MathSciNetCrossRefGoogle Scholar
- 2.Y. Meyer, Ondelettes et fonctions splines Seminaire EDP (Ecole Polytechnique, Paris, 1986)Google Scholar
- 3.I. Daubechies, Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41(7), 909–996 (1988)MathSciNetCrossRefGoogle Scholar
- 4.S. Mallat, A Wavelet Tour of Signal Processing, 2nd edn. (Academic Press, 1999)CrossRefGoogle Scholar
- 5.G.S. Strang, T.Q. Nguyen, Wavelets and Filter Banks (Wellesley Cambridge Press, MA, 1996)MATHGoogle Scholar
- 6.I. Daubechies, Ten Lectures on Wavelets (SIAM, CBMS Series, April 1992)Google Scholar
- 7.R. Coifman, Y. Meyer, S. Quaker, V. Wickerhauser, Signal Processing and Compression with Wavelet Packets (Numerical Algorithms Research Group, New Haven, CT: Yale University, 1990)Google Scholar
- 8.C.K. Chui, An introduction to wavelets, Academic Press,1992Google Scholar
- 9.M. Vetterli, J. Kovacevic, Wavelets and Subband Coding (Prentice-Hall, 1995)Google Scholar
- 10.P. Steffen et al., Theory of regular M-band wavelet bases. IEEE Trans. Signal Process. 41, 3487–3511 (1993)CrossRefGoogle Scholar
- 11.Peter N. Heller, Rank-m wavelet matrices with n vanishing moments. SIAM J. Matrix Anal. 16, 502–518 (1995)MathSciNetCrossRefGoogle Scholar
- 12.Gilbert Strang, Wavelets and dilation equations. SIAM Rev. 31, 614–627 (1989)MathSciNetCrossRefGoogle Scholar
- 13.A. Cohen, I. Daubechies, J.C. Feauveau, Biorthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math. XLV, 485–560 (1992)MathSciNetCrossRefGoogle Scholar
- 14.S.K. Mitra, Digital Signal Processing—A Computer Based Approach (McGraw-Hill Inc, NY, 2006)Google Scholar
- 15.M.V. Wickerhauser, Acoustic Signal Compression with Wavelet Packets, in Wavelets: A Tutorial in Theory and Applications, ed. by C.K. Chui (New York Academic, 1992), pp. 679–700CrossRefGoogle Scholar
- 16.M. Misiti, Y. Misiti, G. Oppenheim, J-M. poggi, Wavelets and Their Applications (ISTEUSA, 2007)Google Scholar
- 17.M.Rao Raghuveer, Ajit S. Bopardikar, Wavelet Transforms: Introduction to Theory and Applications (Pearson Education, Asia, 2000)MATHGoogle Scholar
- 18.Y. Zhao, M.N.S. Swamy, Technique for designing biorthogonal wavelet filters with an application to image compression. Electron. Lett. 35 (18) (September 1999)CrossRefGoogle Scholar
- 19.K.D. Rao, E.I. Plotkin, M.N.S. Swamy, An Hybrid Filter for Restoration of Color Images in the Mixed Noise Environment, in Proceedings of ICASSP, vol. 4 (2002), pp. 3680–3683Google Scholar
- 20.N. Gupta, E.I. Plotkin, M.N.S. Swamy, Wavelet domain-based video noise reduction using temporal dct and hierarchically-adapted thresholding. IEE Proceedings of—Vision, Image and Signal Processing 1(1), 2–12 (2007)Google Scholar
- 21.M.I.H. Bhuiyan, M.O. Ahmad, M.N.S. Swamy, Wavelet-based image denoisingwith the normal inverse gaussian prior and linear minimum mean squared error estimator. IET Image Proc. 2(4), 203–217 (2008)CrossRefGoogle Scholar
- 22.M.I.H. Bhuiyan, M.O. Ahmad, M.N.S. Swamy, Spatially-adaptive thresholding in wavelet domain for despeckling of ultrasound images. IET Image Proc. 3, 147–162 (2009)CrossRefGoogle Scholar
- 23.S.M.M. Rahman, M.O. Ahmad, M.N.S. Swamy, Video denoising based on inter-frame statistical modeling of wavelet coefficients. IEEE Trans. Circuits Syst. Video Technol. 17, 187–198 (2007)CrossRefGoogle Scholar
- 24.S.M.M. Rahman, M.O. Ahmad, M.N.S. Swamy, Bayesian wavelet-based imagedenoising using the gauss-hermite expansion. IEEE Trans. Image Process. 17, 1755–1771 (2008)MathSciNetCrossRefGoogle Scholar
- 25.S.M.M. Rahman, M.O. Ahmad, M.N.S. Swamy, A new statistical detector for dwt-based additive image watermarking using the gauss-hermite expansion. IEEE Trans. Image Process. 18, 1782–1796 (2009)MathSciNetCrossRefGoogle Scholar
- 26.S.M.M. Rahman, M.O. Ahmad, M.N.S. Swamy, Contrast-based fusion of noisy images using discrete wavelet transform. IET Image Proc. 4, 374–384 (2010)MathSciNetCrossRefGoogle Scholar
- 27.D.L. Donoho, L.M. Johnstone, Adapting to unknown smoothness via wavelet shrinkage. J Am. Stat. Soc. 90, 1200–1224 (1995)MathSciNetCrossRefGoogle Scholar
- 28.D.L. Donoho, L.M. Johnstone, Ideal spatial adaptation via wavelet shrinkage. Biometrika 81, 425–455 (1994)MathSciNetCrossRefGoogle Scholar
- 29.L.M. Johnstone, B.W. Silverman, Wavelet threshold estimators for data with correlated noise. J Roy. Stat. Soc. B 59, 319–351 (1997)MathSciNetCrossRefGoogle Scholar
- 30.K.D. Rao, New Approach for Digital Image Watermarking and transmission over Bursty WirelessChannels, in Proceedings of IEEE International Conference on Signal Processing (Beijing, 2010)Google Scholar
- 31.G.K. Wallace, The JPEG still picture compression standard. IEEE Trans. Consumer Electron. 38, xviii–xxxiv (1992)CrossRefGoogle Scholar
- 32.W.B. Pennebaker, J.L. Mitcell, JPEG: Still Image Data Compression Standard (Van Nostrand Reinhold, New York, 1993)Google Scholar
Copyright information
© Springer Nature Singapore Pte Ltd. 2018