Survey on tensor signal algebraic filtering

Signal Processing

Volumn 87, Issue 2, 2007, Pages 237-249

  Muti, Damien ^a   Bourennane, Salah ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

HOSVD; LRTA; Multilinear algebra; Multiway arrays; Subspace method; Tensor; Tensor Wiener filtering; Tucker3 decomposition

Indexed keywords

GAUSSIAN NOISE (ELECTRONIC); MATRIX ALGEBRA; NOISE ABATEMENT; OPTICAL CORRELATION; PRINCIPAL COMPONENT ANALYSIS; TENSORS;

HOSVD; LRTA; MULTILINEAR ALGEBRA; MULTIWAY ARRAYS; SUBSPACE METHOD; TENSOR WIENER FILTERING; TUCKER3 DECOMPOSITION;

SIGNAL FILTERING AND PREDICTION;

EID: 33750146454     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2005.12.016     Document Type: Article

References (46)

1. De Lathauwer L., De Moor B., and Vandewalle J. A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21 (April 2000) 1253-1278
2. N) approximation of higher-order tensors. SIAM J. Matrix Anal. Appl. 21 (April 2000) 1324-1342
3. Golub G.H., and Van Loan C.F. Matrix Computations. third ed. (1996), The John Hopkins University Press, Baltimore
4. Eckart Y., and Young G. The approximation of a matrix by another of lower rank. Psychometrika 1 (1936) 211-218
5. N. Le Bihan, Traitement algébrique des signaux vectoriels: application à la séparation d'ondes sismiques, Ph.D. Thesis, INPG, Grenoble, France, 22 October 2001.
6. Le Bihan N., and Ginolhac G. Three-mode data set analysis using higher order subspace method: application to sonar and seismo-acoustic signal processing. Signal Processing 84 5 (2004) 919-942
7. D. Muti, S. Bourennane, Multidimensional estimation based on a tensor decomposition, in: IEEE Workshop on Statistical Signal Processing, St Louis, MI, USA, September 28-October 1, 2003.
8. D. Muti, S. Bourennane, Multidimensional signal processing using lower rank tensor approximation, in: IEEE International Conference on Acoustics Systems and Signal Processing, Hong Kong, China, April 6-10, 2003.
9. D. Muti, S. Bourennane, Traitement du signal par décomposition tensorielle, in: GRETSI Symposium, Paris, France, September 8-11, 2003.
10. Håstad J. Tensor rank is np-complete. J. Algorithms 11 (September 1990) 644-654
11. Kolda T.G. Orthogonal tensor decomposition. SIAM J. Matrix Anal. Appl. 23 1 (March 2001) 243-255
12. Tucker L.R. Some mathematical notes on three-mode factor analysis. Psychometrika 31 (1966) 279-311
13. Kroonenberg P.M., and De Leeuw J. Principal component analysis of three-mode data by means of alternating least squares algorithms. Psychometrika 45 1 (March 1980) 69-97
14. Alter O., and Golub G.H. Reconstructing the pathways of a cellular system from genome-scale signals by using matrix and tensor computations. Proc. Nat. Acad. Sci. USA 102 49 (October 2005) 17559-17564
15. L. De Lathauwer, Signal processing based on multilinear algebra, Ph.D. Thesis, K.U. Leuven, E.E. Department (ESAT), Belgium, September 1997.
16. Smilde A., Bro R., and Geladi P. Multi-way Analysis: Applications in the Chemical Sciences (2004), Wiley, New York
17. M.A.O. Vasilescu, D. Terzopoulos, Multilinear image analysis for facial recognition, in: IEEE International Conference on Pattern Recognition (ICPR2002), vol. 2, Quebec city, Canada, August 11-15, 2002.
18. H. Wang, N. Ahuja, Facial expression decomposition, in: Ninth IEEE International Conference on Computer Vision (ICCV2003), vol. 2, Nice, France, October 13-16, 2003.
19. Kruskal J.B. Three-way arrays: rank and uniqueness of trilinear decomposition, with application to arithmetic complexity and statistics. Ann. Statist. 18 (1977) 95-138
20. Harshman R.A., and Lundy M.E. Research Methods for Multilmode Data Analysis (1970), Praeger, New York pp. 122-215
21. R. Bro, Multi-way analysis in the food industry, Ph.D. Thesis, Royal Veterinary and Agricultural University, Denmark, 1998.
22. Sidiropoulos N.D., Bro R., and Giannakis G. Parallel factor analysis in sensor array processing. IEEE Trans. Signal Process. 48 8 (August 2000) 2377-2388
23. Sidiropoulos N.D., Giannakis G., and Bro R. Blind parafac receivers for DS-CDMA systems. IEEE Trans. Signal Process. 48 3 (2000) 810-823
24. Kroonenberg P.M. Three-mode Principal Component Analysis (1983), DSWO Press, Leiden
25. Kruskal J.B. Rank, decomposition, and uniqueness for 3-way and N-way arrays, Multiway Data Analysis (1998), Elsevier, North-Holand, Amsterdam, The Netherlands
26. Kofidis E., and Regalia P.A. On the best rank-1 approximation of higher-order supersymmetric tensors. SIAM J. Matrix Anal. Appl. 23 3 (March 2002) 863-884
27. Zhang T., and Golub G.H. Rank-one approximation to high order tensor. SIAM J. Matrix Anal. Appl. 23 2 (2001) 534-550
28. Sidiropoulos N.D., and Bro R. On the uniqueness of multilinear decomposition of N-way arrays. J. Chemometrics 14 (2000) 229-239
29. Muti D., and Bourennane S. Multidimensional filtering based on a tensor approach. Signal Processing J. 85 (May 2005) 2338-2353
30. Muti D., and Bourennane S. Multiway filtering based on fourth order cumulants. Appl. Signal Process. EURASIP 7 (May 2005) 1147-1159
31. Freire F.L.M., and Ulrych T.J. Application of SVD to vertical seismic profiling. Geophysics 53 (1988) 778-785
32. F. Glangeaud, J.-L. Mari, Wave Separation, Technip IFP edition, 1994.
33. Hemon M., and Mace D. The use of Karhunen-Loeve transform in seismic data prospecting. Geophys. Prospecting 26 (1978) 600-626
34. Hsu K. Wave separation and feature extraction of accoustic well-logging waveforme of triaxial recordings by singular value decomposition. Geophysics 55 (1990) 176-184
35. Jackson G.M., Mason I.M., and Greenhalgh S.A. Principal component transforms of triaxial recordings by singular value decomposition. Geophysics 56 4 (1991) 176-184
36. Liu X. Ground roll suppression using the Karhunen-Loeve transform. Geophysics 64 2 (1991) 564-566
37. J. Mars, Séparation d'ondes, Ph.D. Thesis, INPG, Grenoble, France, 1988.
38. D. Muti, Traitement du signal tensoriel. Application aux images en couleurs et aux signaux sismiques, Ph.D. Thesis, Institut Fresnel, Université Paul Cézanne, Aix-Marseille III, Marseille, France, December 2, 2004.
39. Lacoume J.L., Amblard P.O., and Comon P. Statistiques d'ordre supérieur pour le traitement du signal (1997), Masson, Paris
40. Mendel J.M. Tutorial on higher order statistics (spectra) in signal processing and system theory: theoretical results and some applications. Proc. IEEE 79 (March 1991) 278-305
41. Gonen E., and Mendel J.M. Application of cum to array processing-part III: blind beamforming for coherent signal. IEEE Trans. Signal Process. 45 9 (1997) 2252-2264
42. Bourennane S., and Bendjama A. Locating wide band acoustic sources using higher order statistics. Appl. Acoustics 63 (May 2001) 235-251
43. Yuen N., and Friedlander B. Asymptotic performance analysis of blind signal copy using fourth order cumulant. Internat. J. Adaptative Control Signal Process. 48 (March 1996) 239-265
44. Yuen N., and Friedlander B. DOA in multipath: an approach using fourth order cumulant. IEEE Trans. Signal Process. 45 5 (1997) 1253-1263
45. Muti D., Bourennane S., and Guillaume M. SVD-based filtering improvement by means of image rotation. IEEE International Conference on Acoustics Speech and Signal Processing. Montreal, Canada, May 17-21 (2004)
46. Skarbek W. Generalized Hilbert scan in image printing. In: Klette R., and Kropetsh W.G. (Eds). Theoretical Foundations of Computer Vision (1992), Akademik Verlag, Berlin