No Access

A QUINTET SINGULAR VALUE DECOMPOSITION THROUGH EMPIRICAL MODE DECOMPOSITIONS

MIN-SUNG KOH

Department of Engineering and Design, Eastern Washington University, Cheney, WA 99004, USA

https://doi.org/10.1142/S1793536914500101Cited by:0 (Source: Crossref)

Abstract

A particular quintet singular valued decomposition (Quintet-SVD) is introduced in this paper via empirical mode decompositions (EMDs). The Quintet-SVD results in four specific orthogonal matrices with a diagonal matrix of singular values. Furthermore, this paper shows relationships between the Quintet-SVD and traditional SVD, generalized low rank approximations of matrices (GLRAM) of one single matrix, and EMDs. One application of the Quintet-SVD for speech enhancement is shown and compared with an application of traditional SVD.

Keywords:

References

G. H. Golub and C. F. Van Loan , Matrix Computations , 3rd edn. ( The Johns Hopkins University Press , Baltimore, Maryland , 1996 ) . Google Scholar
P. C. Hansen and S. H. Jensen , IEEE Trans. Signal Process. 46 , 1737 ( 1998 ) . Crossref, Google Scholar
N. E. Huang et al. , Proc. R. Soc. Lond. A 454 , 903 ( 1998 ) , DOI: doi:10.1098/rspa.1998.0193 . Crossref, Google Scholar
S. H. Jensen et al. , IEEE Trans. Speech Audio Process. 3 , 439 ( 1995 ) . Crossref, Google Scholar
M. S. Koh and E. Rodriguez-Marek , Speech enhancement of color noise using empirical mode decomposition , The 46th Asilomar Conf. Signal, System and Computers ( 2012 ) . Google Scholar
Y. Kopsinis and S. McLaughlin , EURASIP J. Adv. Signal Process. 2008 , 128293 ( 2008 ) , DOI: 10.1155/2008/128293 . Crossref, Google Scholar
A. Linderhed , SPIE Proc. 4738 , 1 ( 2002 ) . Crossref, Google Scholar
T. K. Moon and W. C. Stirling , Mathematical Methods and Algorithms ( Prentice Hall , Upper Saddle River, NJ , 2000 ) . Google Scholar
B. D. Moor , IEEE Trans. Signal Process. 41 , 2826 ( 1993 ) . Crossref, Google Scholar
J. C. Nunes et al. , Image Vis. Comput. 21 , 1019 ( 2003 ) , DOI: 10.1016/S0262-8856(03)00094-5 . Crossref, Google Scholar
N. U. Rehman and D. P. Mandic , Proc. R. Soc. A 466 , 1291 ( 2010 ) . Crossref, Google Scholar
N. U. Rehman et al. , Adv. Adapt. Data Anal. 2 , 1 ( 2013 ) , DOI: 10.1142/S1793536913500076 . Google Scholar
A. H. Sayed , Adaptive Filters ( John Wiley & Sons, INC. , Hoboken, NJ , 2008 ) . Crossref, Google Scholar
Y. Xu et al. , Proc. R. Soc. A 462 , 3081 ( 2006 ) , DOI: 10.1098/rspa.2006.1700 . Crossref, Google Scholar
Z. Yang, D. Qi and L. Yang, Signal period analysis based on Hilbert–Huang transform and its application to texture analysis, Proc. Third Int. Conf. on Image and Graphics (2004) pp. 430–433. Google Scholar
J. Ye , Mach. Learn. 61 , 167 ( 2005 ) . Crossref, Google Scholar