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Volumn 61, Issue 7, 2015, Pages 4034-4059

Exact and Stable Covariance Estimation From Quadratic Sampling via Convex Programming

Author keywords

Covariance sketching; Energy measurements; Low rank; Phase retrieval; Phase tomography, RIP '2='1; Quadratic measurements; Rank one measurements; Sparsity; Toeplitz

Indexed keywords

CLUSTERING ALGORITHMS; COMMUNICATION CHANNELS (INFORMATION THEORY); CONVEX OPTIMIZATION; COVARIANCE MATRIX; DATA MINING; DIGITAL STORAGE; ELECTRIC POWER MEASUREMENT; INFORMATION THEORY; MATRIX ALGEBRA; PHASE SHIFTERS; PHASE SPACE METHODS; RELAXATION PROCESSES; TOMOGRAPHY; WIRELESS TELECOMMUNICATION SYSTEMS;

EID: 84933059585     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2015.2429594     Document Type: Article
Times cited : (241)

References (61)
  • 1
    • 84905216449 scopus 로고    scopus 로고
    • Estimation of simultaneously structured covariance matrices from quadratic measurements
    • Florence, Italy, May
    • Y. Chen, Y. Chi, and A. J. Goldsmith, "Estimation of simultaneously structured covariance matrices from quadratic measurements", in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Florence, Italy, May 2014, pp. 7669-7673.
    • (2014) Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP) , pp. 7669-7673
    • Chen, Y.1    Chi, Y.2    Goldsmith, A.J.3
  • 2
    • 84906561445 scopus 로고    scopus 로고
    • Robust and universal covariance estimation from quadratic measurements via convex programming
    • Honolulu, HI, USA, Jun./Jul
    • Y. Chen, Y. Chi, and A. J. Goldsmith, "Robust and universal covariance estimation from quadratic measurements via convex programming", in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Honolulu, HI, USA, Jun./Jul. 2014, pp. 2017-2021.
    • (2014) Proc. IEEE Int. Symp. Inf. Theory (ISIT) , pp. 2017-2021
    • Chen, Y.1    Chi, Y.2    Goldsmith, A.J.3
  • 3
    • 0024702515 scopus 로고
    • ESPRIT-estimation of signal parameters via rotational invariance techniques
    • Jul
    • R. Roy and T. Kailath, "ESPRIT-estimation of signal parameters via rotational invariance techniques", IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 7, pp. 984-995, Jul. 1989.
    • (1989) IEEE Trans. Acoust., Speech, Signal Process. , vol.37 , Issue.7 , pp. 984-995
    • Roy, R.1    Kailath, T.2
  • 4
    • 62349123505 scopus 로고    scopus 로고
    • Operator norm consistent estimation of large-dimensional sparse covariance matrices
    • N. E. Karoui, "Operator norm consistent estimation of large-dimensional sparse covariance matrices", Ann. Statist., vol. 36, no. 6, pp. 2717-2756, 2008.
    • (2008) Ann. Statist. , vol.36 , Issue.6 , pp. 2717-2756
    • Karoui, N.E.1
  • 6
    • 40349094869 scopus 로고    scopus 로고
    • 60 GHz wireless communications: Emerging requirements and design recommendations
    • Sep.
    • R. C. Daniels and R. W. Heath, "60 GHz wireless communications: Emerging requirements and design recommendations", IEEE Veh. Technol. Mag., vol. 2, no. 3, pp. 41-50, Sep. 2007.
    • (2007) IEEE Veh. Technol. Mag. , vol.2 , Issue.3 , pp. 41-50
    • Daniels, R.C.1    Heath, R.W.2
  • 7
    • 84876765754 scopus 로고    scopus 로고
    • Compressive spectral estimation for nonstationary random processes
    • May
    • A. Jung, G. Taubock, and F. Hlawatsch, "Compressive spectral estimation for nonstationary random processes", IEEE Trans. Inf. Theory, vol. 59, no. 5, pp. 3117-3138, May 2013.
    • (2013) IEEE Trans. Inf. Theory , vol.59 , Issue.5 , pp. 3117-3138
    • Jung, A.1    Taubock, G.2    Hlawatsch, F.3
  • 9
    • 84865234335 scopus 로고    scopus 로고
    • Compressive wideband power spectrum estimation
    • Sep.
    • D. D. Ariananda and G. Leus, "Compressive wideband power spectrum estimation", IEEE Trans. Signal Process., vol. 60, no. 9, pp. 4775-4789, Sep. 2012.
    • (2012) IEEE Trans. Signal Process. , vol.60 , Issue.9 , pp. 4775-4789
    • Ariananda, D.D.1    Leus, G.2
  • 11
  • 12
  • 13
    • 12044254133 scopus 로고
    • Complex wave-field reconstruction using phase-space tomography
    • Feb.
    • M. G. Raymer, M. Beck, and D. McAlister, "Complex wave-field reconstruction using phase-space tomography", Phys. Rev. Lett., vol. 72, no. 8, p. 1137, Feb. 1994.
    • (1994) Phys. Rev. Lett. , vol.72 , Issue.8 , pp. 1137
    • Raymer, M.G.1    Beck, M.2    McAlister, D.3
  • 14
    • 84860171069 scopus 로고    scopus 로고
    • Experimental compressive phase space tomography
    • L. Tian, J. Lee, S. B. Oh, and G. Barbastathis, "Experimental compressive phase space tomography", Opt. Exp., vol. 20, no. 8, pp. 8296-8308, 2012.
    • (2012) Opt. Exp. , vol.20 , Issue.8 , pp. 8296-8308
    • Tian, L.1    Lee, J.2    Oh, S.B.3    Barbastathis, G.4
  • 15
    • 84878420841 scopus 로고    scopus 로고
    • PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming
    • Aug.
    • E. J. Candès, T. Strohmer, and V. Voroninski, "PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming", Commun. Pure Appl. Math., vol. 66, no. 8, pp. 1241-1274, Aug. 2013.
    • (2013) Commun. Pure Appl. Math. , vol.66 , Issue.8 , pp. 1241-1274
    • Candès, E.J.1    Strohmer, T.2    Voroninski, V.3
  • 16
    • 79961081474 scopus 로고    scopus 로고
    • Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing
    • Y. Shechtman, Y. C. Eldar, A. Szameit, and M. Segev, "Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing", Opt. Exp., vol. 19, no. 16, pp. 14807-14822, 2011.
    • (2011) Opt. Exp. , vol.19 , Issue.16 , pp. 14807-14822
    • Shechtman, Y.1    Eldar, Y.C.2    Szameit, A.3    Segev, M.4
  • 18
    • 84925114763 scopus 로고    scopus 로고
    • Phase retrieval via Wirtinger flow: Theory and algorithms
    • Apr.
    • E. J. Candes, X. Li, and M. Soltanolkotabi, "Phase retrieval via Wirtinger flow: Theory and algorithms", IEEE Trans. Inf. Theory, vol. 61, no. 4, pp. 1985-2007, Apr. 2015.
    • (2015) IEEE Trans. Inf. Theory , vol.61 , Issue.4 , pp. 1985-2007
    • Candes, E.J.1    Li, X.2    Soltanolkotabi, M.3
  • 21
    • 84922369056 scopus 로고    scopus 로고
    • Compressive phase retrieval via generalized approximate message passing
    • Feb.
    • P. Schniter and S. Rangan, "Compressive phase retrieval via generalized approximate message passing", IEEE Trans. Signal Process., vol. 63, no. 4, pp. 1043-1055, Feb. 2015.
    • (2015) IEEE Trans. Signal Process. , vol.63 , Issue.4 , pp. 1043-1055
    • Schniter, P.1    Rangan, S.2
  • 22
    • 85019170540 scopus 로고    scopus 로고
    • A convex formulation for mixed regression with two components: Minimax optimal rates
    • Y. Chen, X. Yi, and C. Caramanis, "A convex formulation for mixed regression with two components: Minimax optimal rates", in Proc. Conf. Learn. Theory (COLT), 2014, pp. 1-45.
    • (2014) Proc. Conf. Learn. Theory (COLT) , pp. 1-45
    • Chen, Y.1    Yi, X.2    Caramanis, C.3
  • 23
    • 84919976187 scopus 로고    scopus 로고
    • Solving quadratic equations via PhaseLift when there are about as many equations as unknowns
    • Oct.
    • E. J. Candès and X. Li, "Solving quadratic equations via PhaseLift when there are about as many equations as unknowns", Found. Comput. Math., vol. 14, no. 5, pp. 1017-1026, Oct. 2013.
    • (2013) Found. Comput. Math. , vol.14 , Issue.5 , pp. 1017-1026
    • Candès, E.J.1    Li, X.2
  • 24
    • 84891329056 scopus 로고    scopus 로고
    • Sparse signal recovery from quadratic measurements via convex programming
    • X. Li and V. Voroninski, "Sparse signal recovery from quadratic measurements via convex programming", SIAM J. Math. Anal., vol. 45, no. 5, pp. 3019-3033, 2013.
    • (2013) SIAM J. Math. Anal. , vol.45 , Issue.5 , pp. 3019-3033
    • Li, X.1    Voroninski, V.2
  • 25
    • 52349092455 scopus 로고    scopus 로고
    • On sparse reconstruction from Fourier and Gaussian measurements
    • Aug.
    • M. Rudelson and R. Vershynin, "On sparse reconstruction from Fourier and Gaussian measurements", Commun. Pure Appl. Math., vol. 61, no. 8, pp. 1025-1045, Aug. 2008.
    • (2008) Commun. Pure Appl. Math. , vol.61 , Issue.8 , pp. 1025-1045
    • Rudelson, M.1    Vershynin, R.2
  • 26
    • 79951886985 scopus 로고    scopus 로고
    • Recovering low-rank matrices from few coefficients in any basis
    • Mar.
    • D. Gross, "Recovering low-rank matrices from few coefficients in any basis", IEEE Trans. Inf. Theory, vol. 57, no. 3, pp. 1548-1566, Mar. 2011.
    • (2011) IEEE Trans. Inf. Theory , vol.57 , Issue.3 , pp. 1548-1566
    • Gross, D.1
  • 27
    • 85162330856 scopus 로고    scopus 로고
    • Universal low-rank matrix recovery from Pauli measurements
    • Y.-K. Liu, "Universal low-rank matrix recovery from Pauli measurements", in Proc. Adv. Neural Inf. Process. Syst., 2011, pp. 1638-1646.
    • (2011) Proc. Adv. Neural Inf. Process. Syst. , pp. 1638-1646
    • Liu, Y.-K.1
  • 28
    • 71049116435 scopus 로고    scopus 로고
    • Exact matrix completion via convex optimization
    • Dec.
    • E. J. Candès and B. Recht, "Exact matrix completion via convex optimization", Found. Comput. Math., vol. 9, no. 6, pp. 717-772, Dec. 2009.
    • (2009) Found. Comput. Math. , vol.9 , Issue.6 , pp. 717-772
    • Candès, E.J.1    Recht, B.2
  • 29
    • 84907189415 scopus 로고    scopus 로고
    • Robust spectral compressed sensing via structured matrix completion
    • Oct.
    • Y. Chen and Y. Chi, "Robust spectral compressed sensing via structured matrix completion", IEEE Trans. Inf. Theory, vol. 60, no. 10, pp. 6576-6601, Oct. 2014.
    • (2014) IEEE Trans. Inf. Theory , vol.60 , Issue.10 , pp. 6576-6601
    • Chen, Y.1    Chi, Y.2
  • 30
    • 79961039847 scopus 로고    scopus 로고
    • High dimensional statistical inference and random matrices
    • Aug.
    • I. M. Johnstone, "High dimensional statistical inference and random matrices", in Proc. Int. Congr. Math., Madrid, Spain, Aug. 2006, pp. 307-333.
    • (2006) Proc. Int. Congr. Math., Madrid, Spain , pp. 307-333
    • Johnstone, I.M.1
  • 31
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr.
    • D. L. Donoho, "Compressed sensing", IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.L.1
  • 32
    • 33947416035 scopus 로고    scopus 로고
    • Near-optimal signal recovery from random projections: Universal encoding strategies?
    • Dec.
    • E. J. Candes and T. Tao, "Near-optimal signal recovery from random projections: Universal encoding strategies?" IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5406-5425, Dec. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candes, E.J.1    Tao, T.2
  • 33
    • 84856400544 scopus 로고    scopus 로고
    • Cyclic feature detection with sub-Nyquist sampling for wideband spectrum sensing
    • Feb.
    • Z. Tian, Y. Tafesse, and B. M. Sadler, "Cyclic feature detection with sub-Nyquist sampling for wideband spectrum sensing", IEEE J. Sel. Topics Signal Process., vol. 6, no. 1, pp. 58-69, Feb. 2012.
    • (2012) IEEE J. Sel. Topics Signal Process. , vol.6 , Issue.1 , pp. 58-69
    • Tian, Z.1    Tafesse, Y.2    Sadler, B.M.3
  • 34
    • 84888618131 scopus 로고    scopus 로고
    • Wideband spectrum sensing from compressed measurements using spectral prior information
    • Dec.
    • D. Romero and G. Leus, "Wideband spectrum sensing from compressed measurements using spectral prior information", IEEE Trans. Signal Process., vol. 61, no. 24, pp. 6232-6246, Dec. 2013.
    • (2013) IEEE Trans. Signal Process. , vol.61 , Issue.24 , pp. 6232-6246
    • Romero, D.1    Leus, G.2
  • 36
    • 84886247578 scopus 로고    scopus 로고
    • Sparsity constrained nonlinear optimization: Optimality conditions and algorithms
    • A. Beck and Y. C. Eldar, "Sparsity constrained nonlinear optimization: Optimality conditions and algorithms", SIAM J. Optim., vol. 23, no. 3, pp. 1480-1509, 2013.
    • (2013) SIAM J. Optim. , vol.23 , Issue.3 , pp. 1480-1509
    • Beck, A.1    Eldar, Y.C.2
  • 37
    • 84867500140 scopus 로고    scopus 로고
    • Recovery of sparse 1-D signals from the magnitudes of their Fourier transform
    • Jul
    • K. Jaganathan, S. Oymak, and B. Hassibi, "Recovery of sparse 1-D signals from the magnitudes of their Fourier transform", in Proc. IEEE ISIT, Jul. 2012, pp. 1473-1477.
    • (2012) Proc. IEEE ISIT , pp. 1473-1477
    • Jaganathan, K.1    Oymak, S.2    Hassibi, B.3
  • 40
    • 79952389882 scopus 로고    scopus 로고
    • Online identification and tracking of subspaces from highly incomplete information
    • Sep./Oct.
    • L. Balzano, R. Nowak, and B. Recht, "Online identification and tracking of subspaces from highly incomplete information", in Proc. Allerton, Sep./Oct. 2010, pp. 704-711.
    • (2010) Proc. Allerton , pp. 704-711
    • Balzano, L.1    Nowak, R.2    Recht, B.3
  • 41
    • 84888116428 scopus 로고    scopus 로고
    • PETRELS: Parallel subspace estimation and tracking by recursive least squares from partial observations
    • Dec.
    • Y. Chi, Y. C. Eldar, and R. Calderbank, "PETRELS: Parallel subspace estimation and tracking by recursive least squares from partial observations", IEEE Trans. Signal Process., vol. 61, no. 23, pp. 5947-5959, Dec. 2013.
    • (2013) IEEE Trans. Signal Process. , vol.61 , Issue.23 , pp. 5947-5959
    • Chi, Y.1    Eldar, Y.C.2    Calderbank, R.3
  • 42
    • 84944416149 scopus 로고    scopus 로고
    • Incremental singular value decomposition of uncertain data with missing values
    • Berlin, Germany: Springer-Verlag
    • M. Brand, "Incremental singular value decomposition of uncertain data with missing values", in Computer Vision-ECCV. Berlin, Germany: Springer-Verlag, 2002, pp. 707-720.
    • (2002) Computer Vision-ECCV , pp. 707-720
    • Brand, M.1
  • 44
    • 78549288866 scopus 로고    scopus 로고
    • Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
    • B. Recht, M. Fazel, and P. A. Parrilo, "Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization", SIAM Rev., vol. 52, no. 3, pp. 471-501, 2010.
    • (2010) SIAM Rev. , vol.52 , Issue.3 , pp. 471-501
    • Recht, B.1    Fazel, M.2    Parrilo, P.A.3
  • 46
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its implications for compressed sensing
    • May
    • E. J. Candès, "The restricted isometry property and its implications for compressed sensing", Comp. Rendus Math., vol. 346, nos. 9-10, pp. 589-592, May 2008.
    • (2008) Comp. Rendus Math. , vol.346 , Issue.9-10 , pp. 589-592
    • Candès, E.J.1
  • 48
    • 69449105428 scopus 로고    scopus 로고
    • Efficient and robust compressed sensing using optimized expander graphs
    • Sep.
    • S. Jafarpour, W. Xu, B. Hassibi, and R. Calderbank, "Efficient and robust compressed sensing using optimized expander graphs", IEEE Trans. Inf. Theory, vol. 55, no. 9, pp. 4299-4308, Sep. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.9 , pp. 4299-4308
    • Jafarpour, S.1    Xu, W.2    Hassibi, B.3    Calderbank, R.4
  • 49
    • 79952823272 scopus 로고    scopus 로고
    • Tight Oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements
    • Apr.
    • E. J. Candes and Y. Plan, "Tight Oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements", IEEE Trans. Inf. Theory, vol. 57, no. 4, pp. 2342-2359, Apr. 2011.
    • (2011) IEEE Trans. Inf. Theory , vol.57 , Issue.4 , pp. 2342-2359
    • Candes, E.J.1    Plan, Y.2
  • 50
    • 55649115527 scopus 로고    scopus 로고
    • A simple proof of the restricted isometry property for random matrices
    • Dec.
    • R. Baraniuk, M. Davenport, R. De Vore, and M. Wakin, "A simple proof of the restricted isometry property for random matrices", Constructive Approx., vol. 28, no. 3, pp. 253-263, Dec. 2008.
    • (2008) Constructive Approx. , vol.28 , Issue.3 , pp. 253-263
    • Baraniuk, R.1    Davenport, M.2    De Vore, R.3    Wakin, M.4
  • 51
    • 0030369277 scopus 로고    scopus 로고
    • Majorizing measures: The generic chaining
    • Jul
    • M. Talagrand, "Majorizing measures: The generic chaining", Ann. Probab., vol. 24, no. 3, pp. 1049-1103, Jul. 1996.
    • (1996) Ann. Probab. , vol.24 , Issue.3 , pp. 1049-1103
    • Talagrand, M.1
  • 52
    • 81255188959 scopus 로고    scopus 로고
    • A probabilistic and RIPless theory of compressed sensing
    • Nov.
    • E. J. Candes and Y. Plan, "A probabilistic and RIPless theory of compressed sensing", IEEE Trans. Inf. Theory, vol. 57, no. 11, pp. 7235-7254, Nov. 2011.
    • (2011) IEEE Trans. Inf. Theory , vol.57 , Issue.11 , pp. 7235-7254
    • Candes, E.J.1    Plan, Y.2
  • 53
    • 84871556743 scopus 로고    scopus 로고
    • Graduate Studies in Mathematics. Providence, RI, USA: AMS
    • T. Tao, Topics in Random Matrix Theory (Graduate Studies in Mathematics). Providence, RI, USA: AMS, 2012.
    • (2012) Topics in Random Matrix Theory
    • Tao, T.1
  • 56
    • 84938533326 scopus 로고    scopus 로고
    • Introduction to the non-asymptotic analysis of random matrices
    • R. Vershynin, "Introduction to the non-asymptotic analysis of random matrices", Compress. Sens., Theory Appl., pp. 210-268, 2012.
    • (2012) Compress. Sens., Theory Appl. , pp. 210-268
    • Vershynin, R.1
  • 57
    • 0038126290 scopus 로고
    • A bound on tail probabilities for quadratic forms in independent random variables
    • D. L. Hanson and F. T. Wright, "A bound on tail probabilities for quadratic forms in independent random variables", Ann. Math. Statist., vol. 42, no. 3, pp. 1079-1083, 1971.
    • (1971) Ann. Math. Statist. , vol.42 , Issue.3 , pp. 1079-1083
    • Hanson, D.L.1    Wright, F.T.2
  • 59
    • 84868526561 scopus 로고    scopus 로고
    • A tail inequality for quadratic forms of sub-Gaussian random vectors
    • Nov.
    • D. Hsu, S. M. Kakade, and T. Zhang, "A tail inequality for quadratic forms of sub-Gaussian random vectors", Electron. Commun. Probab., vol. 17, no. 52, pp. 1-6, Nov. 2012.
    • (2012) Electron. Commun. Probab. , vol.17 , Issue.52 , pp. 1-6
    • Hsu, D.1    Kakade, S.M.2    Zhang, T.3
  • 61
    • 67349153439 scopus 로고    scopus 로고
    • On almost randomizing channels with a short Kraus decomposition
    • Jun.
    • G. Aubrun, "On almost randomizing channels with a short Kraus decomposition", Commun. Math. Phys., vol. 288, no. 3, pp. 1103-1116, Jun. 2009.
    • (2009) Commun. Math. Phys. , vol.288 , Issue.3 , pp. 1103-1116
    • Aubrun, G.1


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