Joint Approximate Diagonalization Method



The joint approximate diagonalization (JAD) method is a means to find an orthogonal matrix U according to the least squares or weighted least squares criteria to diagonalize a data matrix, which can be a covariance matrix or cumulant matrix. Since the 1990s, as the solution of the statistical identification problem, JAD has been used to extract information from the feature structure of the data matrix. For example, the forth-order joint cumulant matrix presented by Cardoso[1], the cumulant matrix generalized by Moreau[2] is greater or equal to the third-order cumulant matrix, SOBI (Second-Order Blind Identification) algorithm developed by Belouchrani, [3, 4] and second derivative matrix of the logarithmic characteristic matrix[5], etc. The major advantage of the JAD method is its high efficiency, Jacobi-like technology alternative least square, parallel factor analysis, and subspace fitting, etc. For infinite samples, JAD can calculate the common feature structure from any part of matrix set A or linear combination of matrix in A ; but for finite samples T, the matrices in set A T can’t accurately share the same feature structure. The viewpoint of statistics, an “averaging” processing should be used to improve accuracy and robustness, then an appropriate weighting can obtain a mean structure. Details will be discussed in Section 5 of this chapter.


Blind Source Separation Mixed Signal Transfer Function Matrix Blind Separation Nonparametric Density Estimation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Cardoso J F (1989) Source separation using higher order moments. In: Proceedings of ICASSP, Glasgow, 1989, pp 2109–2112Google Scholar
  2. [2]
    Moreau E (2001) A generalization of joint-diagonalization criteria for source separation. IEEE Transactions on Signal Processing 49(3): 530–541CrossRefGoogle Scholar
  3. [3]
    Belouchrani A, Amin M G (1998). Blind source separation based on time-frequency signal representation. IEEE Transactions on Signal Processing 46(12): 2888–2898CrossRefGoogle Scholar
  4. [4]
    Belouchrani A, Abed M K, Cardoso J F et al (1997) A blind source separation technique using second-order statistics. IEEE Transactions on Signal Processing 45(2): 434–444CrossRefGoogle Scholar
  5. [5]
    Yeredor A (2000) Blind source separation via the second characteristic function. Signal Processing 80(5): 897–902zbMATHCrossRefGoogle Scholar
  6. [6]
    Cardoso J F, Souloumiac A (1996) Jacobi angles for simultaneous diagonalization. SIAM Journal of Matrix Analysis and Application 17(1): 161–164MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Yeredor A (2002) Non-orthogonal joint diagnalization in the least-squares sense with application in blind source separation. IEEE Transactions on Signal Processing 50(7): 1545–1553MathSciNetCrossRefGoogle Scholar
  8. [8]
    Miyoshi M, Kaneda Y (1988) Inverse filtering of room acoustics. IEEE Transactions on Acoustics, Speech and Signal Processing 36(1): 145–152CrossRefGoogle Scholar
  9. [9]
    Klajman M, Chambers J A (2002) A novel approximate joint diagonalization algorithm. In: Mathematics in signal processing V, Clarendon Press, OxfordGoogle Scholar
  10. [10]
    Belouchrani A, Aded-Meraim K, Amin M G (2004) Blind separation of nonstationary sources. IEEE Signal Processing Letter 11(7): 605–608CrossRefGoogle Scholar
  11. [11]
    Tong L, Xu G H, Hassibi B et al (1995) Blind Channel identification based on second order statistics: A frequency domain approach. IEEE Transactions on Information Theory 41(1): 329–334zbMATHCrossRefGoogle Scholar
  12. [12]
    Schobben D W, Sommen P (2002). A frequency domain blind signal separation method based on decorrelation. IEEE Transactions on Signal Processing 149(5): 253–262Google Scholar
  13. [13]
    Bousbia H, Belouchrani A, Abed K (2001) Jacobi-like algorithm for blind signal separation of convolutive mixturess. Electronics Letters 37(16): 1049–1050CrossRefGoogle Scholar
  14. [14]
    Hild K E, Erdogmus D, Principe J C (2002) Blind source separation of time-varying, instantaneous mixturess using an on-line algorithm. In: IEEE International Conference on Acoustics, Speech and Signal Processing-Proceedings, Orlando, 2002, 1: 993–996MathSciNetGoogle Scholar
  15. [15]
    Wu J B (2003) Study on blind separation of noise signals and method of acoustical feature extraction. Dissertation, Shanghai Jiao Tong University (Chinese)Google Scholar
  16. [16]
    Jia P (2003) Study of blind separation of acoustic signal. Dissertertion, Shanghai Jiao Tong University (Chinese)Google Scholar
  17. [17]
    Wu J B, Chen J, Zhong P (2003) Time frequency-based blind source separation for elimination of cross-terms in Wigner distribution. Electronics Letters 39(5): 475–477CrossRefGoogle Scholar
  18. [18]
    Nuzillard D, Nuzillard J M (2003) Second-order blind source separation in the Fourier space of data. Signal Processing 83(3): 627–631zbMATHCrossRefGoogle Scholar
  19. [19]
    Shi X Z (2003) Signal processing and soft computing. Higher Education Press, Beijing (Chinese)Google Scholar
  20. [20]
    Golub G H, Van Loan C F (1998) Matrix computation. Translated by Lian Q R, et al. Dalian University of Technology Press, DalianGoogle Scholar
  21. [21]
    Xu H X, Chen C C, Shi X Z (2005) Independent component analysis based on nonparametric density estimation on time-frequency domain. In: IEEE International Workshop on Machine Learning for Signal Processing, Mystic, 2005, pp 171–176Google Scholar
  22. [22]
    Holobar A, F’evotte C, Doncarli C et al (2002) Single autoterms selection for blind source separation in time frequency plane. In: Proceedings of EUSIPCO’2002, Toulouse, 2002Google Scholar
  23. [23]
    Balan R, Rosca J (2000) Statistical properties of STFT ratios for two channel systems and applications to blind source separation. In: Proceedings. ICA’2000, Helsinki, 2000Google Scholar
  24. [24]
    Jourjine, Rickard S, Yilmaz O (2000). Blind separation of disjoint orthogonal signals: Demixing N sources from 2 mixtures. In: Proceedings of ICASSP’2000, Istanbul, 2000, 5: 2985–2988Google Scholar
  25. [25]
    Fahmy M F, Osama M H, Amin (2004) Blind source separation using time-frequency distribution. In: Proceedings of 21st National Radio Science Conference (NRSC2004), Cairo, 2004Google Scholar
  26. [26]
    Doyle D J (1977) A proposed methodology for evaluation of the Wiener filtering method of evoked potential estimation. Electroencephalogr. Cli. Neurophysiol., 43: 749–751CrossRefGoogle Scholar
  27. [27]
    de Weerd J P C, Kap J I (1981) A posteriori time-varying filtering of averaged evoked potentials-I: Introduction and conceptual basis. Biol. Cybern., 41: 223–234zbMATHCrossRefGoogle Scholar
  28. [28]
    Lander P (1997) Time-frequency plane Wiener filtering of the high-resolution ECG: Development and application. IEEE Transactions on Biomedical Engineering 44(4): 247–255CrossRefGoogle Scholar
  29. [29]
    Boashash B (2004) Signal enhancement by time-frequency peak filtering. IEEE Transactions on Signal Processing 52(4): 929–937MathSciNetCrossRefGoogle Scholar
  30. [30]
    Kirchauer H (1995) Time-frequency formulation and design of nonstationary Wiener filters. In: IEEE Processing ICASSP-95, Detroit, 1995, pp 1549–1552Google Scholar

Copyright information

© Shanghai Jiao Tong University Press, Shanghai and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Institute of Vibration Shock & NoiseShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations