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Volumn 56, Issue 7, 2010, Pages 3502-3515

Properness and widely linear processing of quaternion random vectors

Author keywords

Canonical correlation analysis (CCA); Properness; Propriety; Quaternions; Second order circularity; Widely linear (WL) processing

Indexed keywords

CANONICAL CORRELATION ANALYSIS; PROPERNESS; QUATERNIONS; SECOND ORDERS; WIDELY LINEAR;

EID: 77953788013     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2048440     Document Type: Article
Times cited : (128)

References (39)
  • 2
    • 33645302958 scopus 로고    scopus 로고
    • Quaternion-music for vectorsensor array processing
    • Apr
    • S. Miron, N. Le Bihan, and J. Mars, "Quaternion-music for vectorsensor array processing," IEEE Trans. Signal Process., vol.54, no.4, pp. 1218-1229, Apr. 2006.
    • (2006) IEEE Trans. Signal Process , vol.54 , Issue.4 , pp. 1218-1229
    • Miron, S.1    Le Bihan, N.2    Mars, J.3
  • 3
    • 2642566022 scopus 로고    scopus 로고
    • Singular value decomposition of quaternion matrices: A new tool for vector-sensor signal processing
    • Jul
    • N. Le Bihan and J. Mars, "Singular value decomposition of quaternion matrices: A new tool for vector-sensor signal processing," Signal Process., vol.84, no.7, pp. 1177-1199, Jul. 2004.
    • (2004) Signal Process , vol.84 , Issue.7 , pp. 1177-1199
    • Le Bihan, N.1    Mars, J.2
  • 4
    • 80053077456 scopus 로고    scopus 로고
    • Optimal separation of polarized signals by quaternionic neural networks
    • presented at the, Florence, Italy
    • N. Le Bihan and S. Buchholz, "Optimal separation of polarized signals by quaternionic neural networks," presented at the XIV European Signal Processing Conference (EUSIPCO), Florence, Italy, 2006.
    • (2006) XIV European Signal Processing Conference (EUSIPCO)
    • Le Bihan, N.1    Buchholz, S.2
  • 5
    • 44349178047 scopus 로고    scopus 로고
    • Polarized signal classification by complex and quaternionic multi-layer perceptrons
    • S. Buchholz and N. Le Bihan, "Polarized signal classification by complex and quaternionic multi-layer perceptrons," Int. J. Neural Syst., vol.18, no.2, pp. 75-85, 2008.
    • (2008) Int. J. Neural Syst , vol.18 , Issue.2 , pp. 75-85
    • Buchholz, S.1    Le Bihan, N.2
  • 7
    • 63449098959 scopus 로고    scopus 로고
    • The quaternion LMS algorithm for adaptive filtering of hypercomplex processes
    • Apr
    • C. Took and D. Mandic, "The quaternion LMS algorithm for adaptive filtering of hypercomplex processes," IEEE Trans. Signal Process., vol.57, no.4, pp. 1316-1327, Apr. 2009.
    • (2009) IEEE Trans. Signal Process , vol.57 , Issue.4 , pp. 1316-1327
    • Took, C.1    Mandic, D.2
  • 8
    • 0027634633 scopus 로고
    • Proper complex random processes with applications to information theory
    • Jul
    • F. Neeser and J. Massey, "Proper complex random processes with applications to information theory," IEEE Trans. Inf. Theory, vol.39, no.7, pp. 1293-1302, Jul. 1993.
    • (1993) IEEE Trans. Inf. Theory , vol.39 , Issue.7 , pp. 1293-1302
    • Neeser, F.1    Massey, J.2
  • 9
    • 0028725278 scopus 로고
    • On circularity
    • Dec
    • B. Picinbono, "On circularity," IEEE Trans. Signal Processing., vol.42, no.12, pp. 3473-3482, Dec. 1994.
    • (1994) IEEE Trans. Signal Processing , vol.42 , Issue.12 , pp. 3473-3482
    • Picinbono, B.1
  • 10
    • 0029359751 scopus 로고
    • Widely linear estimation with complex data
    • Aug
    • B. Picinbono and P. Chevalier, "Widely linear estimation with complex data," IEEE Trans. Signal Process., vol.43, no.8, pp. 2030-2033, Aug. 1995.
    • (1995) IEEE Trans. Signal Process , vol.43 , Issue.8 , pp. 2030-2033
    • Picinbono, B.1    Chevalier, P.2
  • 11
    • 0030270377 scopus 로고    scopus 로고
    • Second-order complex random vectors and normal distributions
    • Oct
    • B. Picinbono, "Second-order complex random vectors and normal distributions," IEEE Trans. Signal Process., vol.44, no.10, pp. 2637-2640, Oct. 1996.
    • (1996) IEEE Trans. Signal Process , vol.44 , Issue.10 , pp. 2637-2640
    • Picinbono, B.1
  • 12
    • 0031078313 scopus 로고    scopus 로고
    • Second-order statistics of complex signals
    • Feb
    • B. Picinbono and P. Bondon, "Second-order statistics of complex signals," IEEE Trans. Signal Process., vol.45, no.2, pp. 411-420, Feb. 1997.
    • (1997) IEEE Trans. Signal Process , vol.45 , Issue.2 , pp. 411-420
    • Picinbono, B.1    Bondon, P.2
  • 13
    • 0029274575 scopus 로고
    • The multivariate complex normal distributionra generalization
    • Mar
    • A. van den Bos, "The multivariate complex normal distributionra generalization," IEEE Trans. Inf. Theory, vol.41, no.3, pp. 537-539, Mar. 1995.
    • (1995) IEEE Trans. Inf. Theory , vol.41 , Issue.3 , pp. 537-539
    • Bos Den A.Van1
  • 14
    • 0037333301 scopus 로고    scopus 로고
    • Second-order analysis of improper complex random vectors and processes
    • Mar
    • P. Schreier and L. Scharf, "Second-order analysis of improper complex random vectors and processes," IEEE Trans. Signal Process., vol.51, no.3, pp. 714-725, Mar. 2003.
    • (2003) IEEE Trans. Signal Process , vol.51 , Issue.3 , pp. 714-725
    • Schreier, P.1    Scharf, L.2
  • 15
    • 33745700923 scopus 로고    scopus 로고
    • A generalized likelihood ratio test for impropriety of complex signals
    • DOI 10.1109/LSP.2006.871858
    • P. Schreier, L. Scharf, and A. Hanssen, "A generalized likelihood ratio test for impropriety of complex signals," IEEE Signal Process. Lett., vol.13, no.7, pp. 433-436, Jul. 2006. (Pubitemid 43997205)
    • (2006) IEEE Signal Processing Letters , vol.13 , Issue.7 , pp. 433-436
    • Schreier, P.J.1    Scharf, L.L.2    Hanssen, A.3
  • 16
    • 61549093032 scopus 로고    scopus 로고
    • On testing for impropriety of complex- valued Gaussian vectors
    • Mar
    • A.Walden and P. Rubin-Delanchy, "On testing for impropriety of complex- valued Gaussian vectors," IEEE Trans. Signal Process., vol.57, no.3, pp. 825-834, Mar. 2009.
    • (2009) IEEE Trans. Signal Process , vol.57 , Issue.3 , pp. 825-834
    • Walden, A.1    Rubin-Delanchy, P.2
  • 17
    • 41849124224 scopus 로고    scopus 로고
    • A unifying discussion of correlation analysis for complex random vectors
    • Apr
    • P. Schreier, "A unifying discussion of correlation analysis for complex random vectors," IEEE Trans. Signal Process., vol.56, no.4, pp. 1327-1336, Apr. 2008.
    • (2008) IEEE Trans. Signal Process , vol.56 , Issue.4 , pp. 1327-1336
    • Schreier, P.1
  • 18
    • 0032245480 scopus 로고    scopus 로고
    • Random vectors with values in quaternion Hilbert spaces
    • N. N. Vakhania, "Random vectors with values in quaternion Hilbert spaces," Theory Probab. Appl., vol.43, no.1, pp. 99-115, 1999.
    • (1999) Theory Probab. Appl , vol.43 , Issue.1 , pp. 99-115
    • Vakhania, N.N.1
  • 20
    • 33745701263 scopus 로고    scopus 로고
    • Complex random vectors and ICA models: Identifiability, uniqueness, and separability
    • Mar
    • J. Eriksson and V. Koivunen, "Complex random vectors and ICA models: Identifiability, uniqueness, and separability," IEEE Trans. Inf. Theory, vol.52, no.3, pp. 1017-1029, Mar. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.3 , pp. 1017-1029
    • Eriksson, J.1    Koivunen, V.2
  • 22
  • 24
    • 0000107975 scopus 로고
    • Relations between two sets of variates
    • H. Hotelling, "Relations between two sets of variates," Biometrika, vol.28, pp. 321-377, 1936.
    • (1936) Biometrika , vol.28 , pp. 321-377
    • Hotelling, H.1
  • 25
    • 0033886042 scopus 로고    scopus 로고
    • Canonical coordinates and the geometry of inference, rate and capacity
    • Mar
    • L. L. Scharf and C. T. Mullis, "Canonical coordinates and the geometry of inference, rate and capacity," IEEE Trans. Signal Process., vol.48, no.3, pp. 824-831, Mar. 2000.
    • (2000) IEEE Trans. Signal Process , vol.48 , Issue.3 , pp. 824-831
    • Scharf, L.L.1    Mullis, C.T.2
  • 26
    • 0000020007 scopus 로고
    • Canonical analysis of several sets of variables
    • J. R. Kettenring, "Canonical analysis of several sets of variables," Biometrika, vol.58, no.3, pp. 433-451, 1971.
    • (1971) Biometrika , vol.58 , Issue.3 , pp. 433-451
    • Kettenring, J.R.1
  • 28
    • 0031540156 scopus 로고    scopus 로고
    • Quaternions and matrices of quaternions
    • F. Zhang, "Quaternions and matrices of quaternions," Linear Algebra Appl., vol.251, pp. 21-57, 1997. (Pubitemid 127379941)
    • (1997) Linear Algebra and Its Applications , vol.251 , pp. 21-57
    • Zhang, F.1
  • 29
    • 0038652528 scopus 로고
    • Quaternions and reflections
    • H. S. M. Coxeter, "Quaternions and reflections," Amer. Math. Month., vol.53, no.3, pp. 136-146, 1946.
    • (1946) Amer. Math. Month , vol.53 , Issue.3 , pp. 136-146
    • Coxeter, H.S.M.1
  • 30
    • 0031279853 scopus 로고    scopus 로고
    • Characterizing the response of PET and fMRI data using multivariate linear models
    • Nov
    • K. J. Worsley, J.-B. Poline, K. J. Friston, and A. C. Evans, "Characterizing the response of PET and fMRI data using multivariate linear models," NeuroImage, vol.6, no.4, pp. 305-319, Nov. 1997.
    • (1997) NeuroImage , vol.6 , Issue.4 , pp. 305-319
    • Worsley, K.J.1    Poline, J.-B.2    Friston, K.J.3    Evans, A.C.4
  • 31
    • 12444339493 scopus 로고    scopus 로고
    • Detection and estimation of improper complex random signals
    • Jan
    • P. Schreier, L. Scharf, and C. Mullis, "Detection and estimation of improper complex random signals," IEEE Trans. Inf. Theory, vol.51, no.1, pp. 306-312, Jan. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.1 , pp. 306-312
    • Schreier, P.1    Scharf, L.2    Mullis, C.3
  • 32
    • 77953768656 scopus 로고    scopus 로고
    • Detection and estimation of Gaussian proper quaternion valued random processes
    • presented at the, Cirencester, U.K., Dec
    • N. Le Bihan and P. O. Amblard, "Detection and estimation of Gaussian proper quaternion valued random processes," presented at the 7th IMA Conf. Mathematics in Signal Processing, Cirencester, U.K., Dec. 2006.
    • (2006) 7th IMA Conf. Mathematics in Signal Processing
    • Le Bihan, N.1    Amblard, P.O.2
  • 34
    • 33845646938 scopus 로고    scopus 로고
    • A learning algorithm for adaptive canonical correlation analysis of several data sets
    • Jan
    • J. Vía, I. Santamaría, and J. Pérez, "A learning algorithm for adaptive canonical correlation analysis of several data sets," Neural Netw., vol.20, no.1, pp. 139-152, Jan. 2007.
    • (2007) Neural Netw , vol.20 , Issue.1 , pp. 139-152
    • Vía, J.1    Santamaría, I.2    Pérez, J.3
  • 35
    • 34347389448 scopus 로고    scopus 로고
    • Deterministic CCA-based algorithms for blind equalization of FIR-MIMO channels
    • Jul
    • J. Vía, I. Santamaría, and J. Pérez, "Deterministic CCA-based algorithms for blind equalization of FIR-MIMO channels," IEEE Trans. Signal Process., vol.55, no.7, pp. 3867-3878, Jul. 2007.
    • (2007) IEEE Trans. Signal Process , vol.55 , Issue.7 , pp. 3867-3878
    • Vía, J.1    Santamaría, I.2    Pérez, J.3
  • 37
    • 0020183044 scopus 로고
    • Estimation of structured covariance matrices
    • Sep
    • J. Burg, D. Luenberger, and D. Wenger, "Estimation of structured covariance matrices," Proc. IEEE, vol.70, no.7, pp. 963-974, Sep. 1982.
    • (1982) Proc. IEEE , vol.70 , Issue.7 , pp. 963-974
    • Burg, J.1    Luenberger, D.2    Wenger, D.3
  • 39
    • 0010134082 scopus 로고    scopus 로고
    • Hoboken, NJ:Wiley, , ch. Entropic contrasts for source separation: geometry and stability
    • J. Cardoso, Unsupervised Adaptive Filtering, Volume 1, Blind Source Separation. Hoboken, NJ:Wiley, 2000, vol.1, ch. Entropic contrasts for source separation: geometry and stability, pp. 139-190.
    • (2000) Unsupervised Adaptive Filtering Volume 1, Blind Source Separation , vol.1 , pp. 139-190
    • Cardoso, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.