Separation and Reproduction of Mixed Images Using 2-D Complex Wavelet Transform

Abstract:

The differences method between 1-D wavelet transform and 2-D wavelet transform in image processing is discussed. Both proposed method uses the quotient of complex valued time-frequency information of observed signals to detect the number of sources. No less number of observed signals than the detected number of sources is needed to separate sources. The assumption on sources is quite general independence in the time-frequency plane, which is different from that of independent component analysis. Using the same given Algorithm and parameters for both method, the result on separated images are compared.

• Periodical: Applied Mechanics and Materials (Volume 36)
• Pages: 466-475
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.36.466
• Online since: October 2010
• Authors: Tsutomu Matsuura, Amirul Faiz, Kouji Kiryu
• Keywords: 2-D Wavelet Transform, Blind Source Separation (BSS), ICA, Image De-Noising

References

[1] Akira Morimoto, Keiko Fujita, and Ryuichi Ashino: Blind source separation using quotient signal method (Journal of Latex Class Files, Vol. 1, N0. 11, November 2002).

[2] R. Ashino, C. A. Berenstein, K. Fujita, A. Morimoto, A. Morimoto,D. Napoletani, and Y. Takei, Mathematical background for a method on quotient signal decomposition, submitted.

DOI: 10.1080/00036810701286288

[3] R. Balan and J. Rosca, Statistical properties of STFT ratios for two channel systems and applications to blind source separation, Proceedings ICA 2000, 19-22 June 2000, Helsinki, Finland.

[4] C. Cherry, On human communication, the revised edition, The MIT Press, (1980).

[5] S. Choi and A. Cichoki, Blind separation of nonstationary sources in noisy mixtures, Electron. Lett., 36-9, 848–849, (2000).

DOI: 10.1049/el:20000623

[6] S. Choi and A. Cichoki, Blind separation of nonstationary sources in noisy mixtures, Electron. Lett., 36-9, 848–849, (2000).

DOI: 10.1049/el:20000623

[7] D. Gabor, Theory of communication, J. IEE, 93, 429–457, (1946).

[8] K. Fujita, Y. Takei, A. Morimoto, R. Ashino and M. Morimoto, Blind source separation on a time-frequency space—mathematical background—, IEICE Technical Report EA2005-12, 37–42, 2005. (In Japanese. ).

DOI: 10.1016/j.amc.2006.08.172

[9] D. Napoletani, C.A. Berenstein and P.S. Krishnaprasad, Quotient signal decomposition and order estimation, TECHNICAL RESEARCH REPORT of University of Maryland,　http: /www. isr. umd. edu, TR 2002-47.

[10] A. Jourjine, S. Rickard and O. Yilmaz, Blind separation of disjoint orthogonal signals: Demixing n sources from 2 mixtures, Proceedings IEEE International Conference on Acoustics, Speech and Signal Processing, 5-9 June 2000, Istanbul, Turkey, IEEE Press, (2000).

DOI: 10.1109/icassp.2000.861162