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Volumn 60, Issue 12, 2012, Pages 6340-6353

Simultaneous codeword optimization (SimCO) for dictionary update and learning

Author keywords

Dictionary learning; Grassmann manifold; optimization; singularity; sparse representation

Indexed keywords

CODE-WORDS; CODEWORD; DICTIONARY LEARNING; GRASSMANN MANIFOLD; LINEAR COMBINATIONS; LOCAL MINIMUMS; OVER-COMPLETE; SECOND ORDER OPTIMIZATION; SINGULAR POINTS; SINGULARITY; SPARSE CODING; SPARSE REPRESENTATION; SPARSITY PATTERNS; TRAINING SIGNAL;

EID: 84870486964     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2012.2215026     Document Type: Article
Times cited : (117)

References (68)
  • 1
    • 0025604930 scopus 로고
    • Forming sparse representations by local anti-Hebbian learning
    • P. Foldiak, "Forming sparse representations by local anti-Hebbian learning," Biolog. Cybern., vol. 64, pp. 165-170, 1990.
    • (1990) Biolog. Cybern , vol.64 , pp. 165-170
    • Foldiak, P.1
  • 2
    • 0034133184 scopus 로고    scopus 로고
    • Learning overcomplete representations
    • M. S. Lewicki and T. J. Sejnowski, "Learning overcomplete representations," Neural Comput., vol. 12, no. 2, pp. 337-365, 2000.
    • (2000) Neural Comput , vol.12 , Issue.2 , pp. 337-365
    • Lewicki, M.S.1    Sejnowski, T.J.2
  • 3
    • 8144227433 scopus 로고    scopus 로고
    • Ph.D., Computational and Applied Math. Dept., Univ. Texas, Austin
    • J. Tropp, "Topics in Sparse Approximations," Ph.D., Computational and Applied Math. Dept., Univ. Texas, Austin, 2004.
    • (2004) Topics in Sparse Approximations
    • Tropp, J.1
  • 4
    • 70449491909 scopus 로고    scopus 로고
    • Learning real and complex overcomplete representations fromthe statistics of natural images
    • B.A. Olshausen, C. F. Cadieu, and D. K. Warland, "Learning real and complex overcomplete representations fromthe statistics of natural images," Proc. SPIE, vol. 7446, pp. 74460S-74460S-11, 2009.
    • (2009) Proc. SPIE , vol.7446
    • Olshausen, B.A.1    Cadieu, C.F.2    Warland, D.K.3
  • 5
    • 0029938380 scopus 로고    scopus 로고
    • Emergence of simple-cell receptive field properties by learning a sparse code for natural images
    • DOI 10.1038/381607a0
    • B. A. Olshausen and D. J. Field, "Emergence of simple-cell receptive field properties by learning a sparse code for natural images," Nature, vol. 381, pp. 607-609, 1996. (Pubitemid 26177476)
    • (1996) Nature , vol.381 , Issue.6583 , pp. 607-609
    • Olshausen, B.A.1    Field, D.J.2
  • 6
    • 79952917189 scopus 로고    scopus 로고
    • Dictionary learning for stereo image representation
    • I. Tošic and P. Frossard, "Dictionary learning for stereo image representation," IEEE Trans. Image Process., vol. 20, no. 4, pp. 921-934, 2011.
    • (2011) IEEE Trans. Image Process , vol.20 , Issue.4 , pp. 921-934
    • Tošic, I.1    Frossard, P.2
  • 7
    • 0000660321 scopus 로고    scopus 로고
    • Blind source separation by sparse decomposition in a signal dictionary
    • DOI 10.1162/089976601300014385
    • M. Zibulevsky and B. A. Pearlmutter, "Blind source separation by sparse decomposition of a signal dictionary," Neural Comput., vol. 13, no. 4, pp. 863-882, 2001. (Pubitemid 33594308)
    • (2001) Neural Computation , vol.13 , Issue.4 , pp. 863-882
    • Zibulevsky, M.1    Pearlmutter, B.A.2
  • 8
    • 0036293554 scopus 로고    scopus 로고
    • Sparse decomposition of stereo signals with matching pursuit and application to blind separation of more than two sources from a stereo mixture
    • R. Gribonval, "Sparse decomposition of stereo signals with matching pursuit and application to blind separation of more than two sources from a stereo mixture," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., 2002, vol. 3, pp. 3057-3060.
    • (2002) Proc IEEE Int. Conf. Acoust., Speech Signal Process , vol.3 , pp. 3057-3060
    • Gribonval, R.1
  • 10
    • 33750383209 scopus 로고    scopus 로고
    • K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation
    • DOI 10.1109/TSP.2006.881199
    • M. Aharon, M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation," IEEE Trans. Signal Process., vol. 54, no. 11, pp. 4311-4322, 2006. (Pubitemid 44637761)
    • (2006) IEEE Transactions on Signal Processing , vol.54 , Issue.11 , pp. 4311-4322
    • Aharon, M.1    Elad, M.2    Bruckstein, A.3
  • 11
    • 80051759153 scopus 로고    scopus 로고
    • Fast dictionary learning for sparse representations of speech signals
    • M. G. Jafari and M. D. Plumbley, "Fast dictionary learning for sparse representations of speech signals," IEEE J. Sel. Topics in Signal Process., vol. 5, no. 5, pp. 1025-1031, 2011.
    • (2011) IEEE J. Sel. Topics in Signal Process , vol.5 , Issue.5 , pp. 1025-1031
    • Jafari, M.G.1    Plumbley, M.D.2
  • 12
    • 2942694091 scopus 로고    scopus 로고
    • Dictionary design for matching pursuit and application to motion-compensated video coding
    • P. Schmid-Saugeon and A. Zakhor, "Dictionary design for matching pursuit and application to motion-compensated video coding," IEEE Trans. Circuits Syst. Video Technol., vol. 14, no. 6, pp. 880-886, 2004.
    • (2004) IEEE Trans. Circuits Syst. Video Technol , vol.14 , Issue.6 , pp. 880-886
    • Schmid-Saugeon, P.1    Zakhor, A.2
  • 13
    • 47649089615 scopus 로고    scopus 로고
    • Semantic coding by supervised dimensionality reduction
    • E. Kokiopoulou and P. Frossard, "Semantic coding by supervised dimensionality reduction," IEEE Trans. Multimed., vol. 10, no. 5, pp. 806-818, 2008.
    • (2008) IEEE Trans. Multimed , vol.10 , Issue.5 , pp. 806-818
    • Kokiopoulou, E.1    Frossard, P.2
  • 14
    • 77952744810 scopus 로고    scopus 로고
    • Sparse representations in audio and music: From coding to source separation
    • M. D. Plumbley, T. Blumensath, L. Daudet, R. Gribonval, and M. E. Davies, "Sparse representations in audio and music: From coding to source separation," Proc. IEEE, vol. 98, no. 6, pp. 995-1005, 2010.
    • (2010) Proc IEEE , vol.98 , Issue.6 , pp. 995-1005
    • Plumbley, M.D.1    Blumensath, T.2    Daudet, L.3    Gribonval, R.4    Davies, M.E.5
  • 19
    • 80051750059 scopus 로고    scopus 로고
    • Greedy dictionary selection for sparse representation
    • V. Cevher and A. Krause, "Greedy dictionary selection for sparse representation," IEEE J. Sel. Topics Signal Process., vol. 5, no. 5, pp. 979-988, 2011.
    • (2011) IEEE J. Sel. Topics Signal Process , vol.5 , Issue.5 , pp. 979-988
    • Cevher, V.1    Krause, A.2
  • 21
    • 77952678579 scopus 로고    scopus 로고
    • Applications of sparse representation and compressive sensing
    • R. G. Baraniuk, E. J. Candès, M. Elad, and Y. Ma, "Applications of sparse representation and compressive sensing," Proc. IEEE, vol. 98, no. 6, pp. 906-909, 2010.
    • (2010) Proc IEEE , vol.98 , Issue.6 , pp. 906-909
    • Baraniuk, R.G.1    Candès, E.J.2    Elad, M.3    Ma, Y.4
  • 23
    • 0027842081 scopus 로고
    • Matching pursuits with time-frequency dictionaries
    • S. G. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397-3415, 1993.
    • (1993) IEEE Trans. Signal Process , vol.41 , Issue.12 , pp. 3397-3415
    • Mallat, S.G.1    Zhang, Z.2
  • 24
    • 0027814133 scopus 로고
    • Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition
    • Y. C. Pati, R. Rezaiifar, and P. S.Krishnaprasad, "Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition," in Proc. IEEE Asilomar Conf. Signals, Syst. Comput., 1993, pp. 40-44.
    • (1993) Proc IEEE Asilomar Conf. Signals, Syst. Comput , pp. 40-44
    • Pati, Y.C.1    Rezaiifar, R.2    Krishnaprasad, P.S.3
  • 25
    • 64649083745 scopus 로고    scopus 로고
    • Signal recovery from random measurements via orthogonal matching pursuit
    • J. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol. 53, no. 12, pp. 4655-4666, 2007.
    • (2007) IEEE Trans. Inf. Theory , vol.53 , Issue.12 , pp. 4655-4666
    • Tropp, J.1    Gilbert, A.C.2
  • 26
    • 65749110333 scopus 로고    scopus 로고
    • Subspace pursuit for compressive sensing signal reconstruction
    • W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Trans. Inf. Theory, vol. 55, pp. 2230-2249, 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , pp. 2230-2249
    • Dai, W.1    Milenkovic, O.2
  • 27
    • 62749175137 scopus 로고    scopus 로고
    • Cosamp: Iterative signal recovery from incomplete and inaccurate samples
    • May
    • D. Needell and J. A. Tropp, "Cosamp: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comp. Harmon. Anal., vol. 26, no. 3, pp. 301-321, May 2009.
    • (2009) Appl. Comp. Harmon. Anal , vol.26 , Issue.3 , pp. 301-321
    • Needell, D.1    Tropp, J.A.2
  • 28
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • R. Tibshirani, "Regression shrinkage and selection via the lasso," J. R. Stat. Soc. Ser. B (Method.), vol. 58, no. 1, pp. 267-288, 1996.
    • (1996) J. R. Stat. Soc. Ser. B (Method , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 29
    • 0031102203 scopus 로고    scopus 로고
    • Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm
    • I. Gorodnitsky and B. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process., vol. 45, no. 3, pp. 600-616, 1997. (Pubitemid 127765947)
    • (1997) IEEE Transactions on Signal Processing , vol.45 , Issue.3 , pp. 600-616
    • Gorodnitsky, I.F.1    Rao, B.D.2
  • 31
    • 85032751971 scopus 로고    scopus 로고
    • The dual-tree complex wavelet transform
    • DOI 10.1109/MSP.2005.1550194
    • I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, "The dual-tree complex wavelet transform," IEEE Signal Process. Mag., vol. 22, no. 6, pp. 123-151, 2005. (Pubitemid 46404908)
    • (2005) IEEE Signal Processing Magazine , vol.22 , Issue.6 , pp. 123-151
    • Selesnick, I.W.1    Baraniuk, R.G.2    Kingsbury, N.G.3
  • 32
    • 0003306887 scopus 로고    scopus 로고
    • Curvelets-A surprisingly effective nonadaptive representation for objects with edges
    • A. CohenC. Rabut, and L. Schumaker, Eds. Nashville, TN: Vanderbilt Univ. Press
    • E. J. Candès and D. L. Donoho, "Curvelets-A surprisingly effective nonadaptive representation for objects with edges," in Curves and Surface Fitting: Saint-Malo Proceedings, A. Cohen, C. Rabut, and L. Schumaker, Eds. Nashville, TN: Vanderbilt Univ. Press, 2000, pp. 105-120.
    • (2000) Curves and Surface Fitting: Saint-Malo Proceedings , pp. 105-120
    • Candès, E.J.1    Donoho, D.L.2
  • 33
    • 28944432472 scopus 로고    scopus 로고
    • The contourlet transform: An efficient directional multiresolution image representation
    • DOI 10.1109/TIP.2005.859376
    • M. N. Do and M. Vetterli, "The contourlet transform: An efficient directional multiresolution image representation," IEEE Trans. Image Process., vol. 14, no. 12, pp. 2091-2106, 2005. (Pubitemid 41781516)
    • (2005) IEEE Transactions on Image Processing , vol.14 , Issue.12 , pp. 2091-2106
    • Do, M.N.1    Vetterli, M.2
  • 34
    • 17544369568 scopus 로고    scopus 로고
    • Sparse geometric image representations with bandelets
    • DOI 10.1109/TIP.2005.843753
    • E. LePennec and S. Mallat, "Sparse geometric image representations with bandelets," IEEE Trans. Image Process., vol. 14, no. 4, pp. 423-438, 2005. (Pubitemid 40552380)
    • (2005) IEEE Transactions on Image Processing , vol.14 , Issue.4 , pp. 423-438
    • Le Pennec, E.1    Mallat, S.2
  • 35
    • 0030779611 scopus 로고    scopus 로고
    • Sparse coding with an overcomplete basis set: A strategy employed by V1?
    • DOI 10.1016/S0042-6989(97)00169-7, PII S0042698997001697
    • B. A. Olshausen and D. J. Field, "Sparse coding with an overcomplete basis set: A strategy employed by V1," Vis. Res, vol. 37, no. 23, pp. 3311-3325, 1997. (Pubitemid 27493805)
    • (1997) Vision Research , vol.37 , Issue.23 , pp. 3311-3325
    • Olshausen, B.A.1    Field, D.J.2
  • 38
    • 3543103176 scopus 로고    scopus 로고
    • Sparse Bayesian learning for basis selection
    • D. P. Wipf and B. D. Rao, "Sparse Bayesian learning for basis selection," IEEE Trans. Signal Process., vol. 52, no. 8, pp. 2153-2164, 2004.
    • (2004) IEEE Trans. Signal Process , vol.52 , Issue.8 , pp. 2153-2164
    • Wipf, D.P.1    Rao, B.D.2
  • 39
    • 38149057402 scopus 로고    scopus 로고
    • Dictionary learning for L1-exact sparse coding
    • M. D. Plumbley, "Dictionary learning for L1-exact sparse coding," Lect. Notes Comput. Sci, vol. 4666, pp. 406-413, 2007.
    • (2007) Lect. Notes Comput. Sci , vol.4666 , pp. 406-413
    • Plumbley, M.D.1
  • 40
    • 79961187754 scopus 로고    scopus 로고
    • Speech denoising based on a greedy adaptive dictionary algorithm
    • M. G. Jafari andM. D. Plumbley, "Speech denoising based on a greedy adaptive dictionary algorithm," in Proc. Conf. Eur. Signal Process., 2009, pp. 1423-1426.
    • (2009) Proc. Conf. Eur. Signal Process , pp. 1423-1426
    • Jafari, M.G.1    Plumbley, M.D.2
  • 41
    • 77953788888 scopus 로고    scopus 로고
    • Dictionary identification-Sparse matrix factorization via l1 minimization
    • R. Gribonval and K. Schnass, "Dictionary identification-Sparse matrix factorization via l1 minimization," IEEE Trans. Inf. Theory, vol. 56, no. 7, pp. 3523-3539, 2010.
    • (2010) IEEE Trans. Inf. Theory , vol.56 , Issue.7 , pp. 3523-3539
    • Gribonval, R.1    Schnass, K.2
  • 43
    • 77952714665 scopus 로고    scopus 로고
    • Dictionaries for sparse representation modelling
    • R. Rubinstein, A.M. Bruckstein, and M. Elad, "Dictionaries for sparse representation modelling," Proc. IEEE, vol. 98, no. 6, pp. 1045-1057, 2010.
    • (2010) Proc IEEE , vol.98 , Issue.6 , pp. 1045-1057
    • Rubinstein, R.1    Bruckstein, A.M.2    Elad, M.3
  • 44
    • 37849188832 scopus 로고    scopus 로고
    • Family of iterative LS-based dictionary learning algorithms, ILS-DLA, for sparse signal representation
    • DOI 10.1016/j.dsp.2006.02.002, PII S105120040600025X
    • K. Engan, K. Skretting, and J. H. Husøy, "Family of iterative LS-based dictionary learning algorithms, ILS-DLA, for sparse signal representation," Dig. Signal Process., vol. 17, no. 1, pp. 32-49, 2007. (Pubitemid 44828547)
    • (2007) Digital Signal Processing: A Review Journal , vol.17 , Issue.1 , pp. 32-49
    • Engan, K.1    Skretting, K.2    Husoy, J.H.3
  • 45
    • 77949403269 scopus 로고    scopus 로고
    • Recursive least squares dictionary learning algorithm
    • K. Skretting and K. Engan, "Recursive least squares dictionary learning algorithm," IEEE Trans. Signal Process., vol. 58, no. 4, pp. 2121-2130, 2010.
    • (2010) IEEE Trans. Signal Process , vol.58 , Issue.4 , pp. 2121-2130
    • Skretting, K.1    Engan, K.2
  • 46
    • 66849115117 scopus 로고    scopus 로고
    • Dictionary learning for sparse approximations with the majorization method
    • M. Yaghoobi, T. Blumensath, and M. E. Davies, "Dictionary learning for sparse approximations with the majorization method," IEEE Trans. Signal Process., vol. 57, no. 6, pp. 2178-2191, 2009.
    • (2009) IEEE Trans. Signal Process , vol.57 , Issue.6 , pp. 2178-2191
    • Yaghoobi, M.1    Blumensath, T.2    Davies, M.E.3
  • 47
    • 70450233548 scopus 로고    scopus 로고
    • Parametric dictionary design for sparse coding
    • M. Yaghoobi, L. Daudet, and M. E. Davies, "Parametric dictionary design for sparse coding," IEEE Trans. Signal Process., vol. 57, no. 12, pp. 4800-4810, 2009.
    • (2009) IEEE Trans. Signal Process , vol.57 , Issue.12 , pp. 4800-4810
    • Yaghoobi, M.1    Daudet, L.2    Davies, M.E.3
  • 49
    • 70349146040 scopus 로고    scopus 로고
    • Learning transformational invariants from time-varying natural images
    • C. Cadieu and B. A. Olshausen, "Learning transformational invariants from time-varying natural images," in Proc. Conf. Neur. Inf. Process. Syst., 2009, vol. 21, pp. 209-216.
    • (2009) Proc. Conf. Neur. Inf. Process. Syst , vol.21 , pp. 209-216
    • Cadieu, C.1    Olshausen, B.A.2
  • 52
    • 67349251766 scopus 로고    scopus 로고
    • Sparse and redundant modeling of image content using an image-signature-dictionary
    • M. Aharon and M. Elad, "Sparse and redundant modeling of image content using an image-signature-dictionary," SIAM J. Imag. Sci., vol. 1, no. 3, pp. 228-247, 2008.
    • (2008) SIAM J. Imag. Sci , vol.1 , Issue.3 , pp. 228-247
    • Aharon, M.1    Elad, M.2
  • 54
    • 0347968052 scopus 로고    scopus 로고
    • Sparse representations in unions of bases
    • R. Gribonval and M. Nielsen, "Sparse representations in unions of bases," IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3320-3325, 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.12 , pp. 3320-3325
    • Gribonval, R.1    Nielsen, M.2
  • 56
    • 80051734077 scopus 로고    scopus 로고
    • Robust and fast learning of sparse codes with stochastic gradient descent
    • K. Labusch, E. Barth, and T. Martinetz, "Robust and fast learning of sparse codes with stochastic gradient descent," IEEE J. Sel. Top. Signal Process., vol. 5, no. 5, pp. 1048-1060, 2011.
    • (2011) IEEE J. Sel. Top. Signal Process , vol.5 , Issue.5 , pp. 1048-1060
    • Labusch, K.1    Barth, E.2    Martinetz, T.3
  • 57
    • 76749107542 scopus 로고    scopus 로고
    • Online learning for matrix factorization and sparse coding
    • J.Mairal, F. Bach, J. Ponce, andG. Sapiro, "Online learning for matrix factorization and sparse coding," J. Mach. Learn. Res., vol. 11, pp. 16-60, 2010.
    • (2010) J. Mach. Learn. Res , vol.11 , pp. 16-60
    • Mairal, J.1    Bach, F.2    Ponce, J.3    Sapiro, G.4
  • 58
    • 72149118713 scopus 로고    scopus 로고
    • Learning bimodal structure in audio-visual data
    • G. Monaci, P. Vandergheynst, and F. T. Sommer, "Learning bimodal structure in audio-visual data," IEEE Trans. Neural Netw., vol. 20, no. 12, pp. 1898-1910, 2009.
    • (2009) IEEE Trans. Neural Netw , vol.20 , Issue.12 , pp. 1898-1910
    • Monaci, G.1    Vandergheynst, P.2    Sommer, F.T.3
  • 59
    • 77954713616 scopus 로고    scopus 로고
    • Blind audiovisual source separation based on sparse redundant representations
    • A. L. Casanovas, G. Monaci, P. Vandergheynst, and R. Gribonval, "Blind audiovisual source separation based on sparse redundant representations," IEEE Trans. Multimed., vol. 12, no. 5, pp. 358-371, 2010.
    • (2010) IEEE Trans. Multimed , vol.12 , Issue.5 , pp. 358-371
    • Casanovas, A.L.1    Monaci, G.2    Vandergheynst, P.3    Gribonval, R.4
  • 60
    • 85032751780 scopus 로고    scopus 로고
    • Dictionary learning: What is the right representation for my signal
    • Mar.
    • I. Tošic and P. Frossard, "Dictionary learning: What is the right representation for my signal," IEEE Signal Process. Mag., vol. 28, no. 2, pp. 27-38, Mar. 2011.
    • (2011) IEEE Signal Process. Mag , vol.28 , Issue.2 , pp. 27-38
    • Tošic, I.1    Frossard, P.2
  • 61
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • DOI 10.1109/TIT.2005.858979
    • E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005. (Pubitemid 41800353)
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candes, E.J.1    Tao, T.2
  • 63
    • 84855697931 scopus 로고    scopus 로고
    • A geometric approach to lowrank matrix completion
    • Jan.
    • W. Dai, E. Kerman, and O. Milenkovic, "A geometric approach to lowrank matrix completion," IEEE Trans. Inf. Theory, vol. 58, no. 1, pp. 237-247, Jan. 2012.
    • (2012) IEEE Trans. Inf. Theory , vol.58 , Issue.1 , pp. 237-247
    • Dai, W.1    Kerman, E.2    Milenkovic, O.3
  • 67
    • 33751379736 scopus 로고    scopus 로고
    • Image denoising via sparse and redundant representations over learned dictionaries
    • DOI 10.1109/TIP.2006.881969
    • M. Elad and M. Aharon, "Image denoising via sparse and redundant representations over learned dictionaries," IEEE Trans. Image Process., vol. 15, no. 12, pp. 3736-3745, Dec. 2006. (Pubitemid 44811686)
    • (2006) IEEE Transactions on Image Processing , vol.15 , Issue.12 , pp. 3736-3745
    • Elad, M.1    Aharon, M.2
  • 68
    • 41049094191 scopus 로고    scopus 로고
    • Quantization bounds on Grassmann manifolds and applications to MIMO communications
    • DOI 10.1109/TIT.2007.915691
    • W. Dai, Y. Liu, and B. Rider, "Quantization bounds on Grassmann manifolds and applications to MIMO systems," IEEE Trans. Inf. Theory, vol. 54, no. 3, pp. 1108-1123, Mar. 2008. (Pubitemid 351418908)
    • (2008) IEEE Transactions on Information Theory , vol.54 , Issue.3 , pp. 1108-1123
    • Dai, W.1    Liu, Y.2    Rider, B.3


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