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Tytuł artykułu

Phase retrieval using random cubatures and fusion frames of positive semidefinite matrices

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EN

Abstrakty

EN
As a generalization of the standard phase retrieval problem,we seek to reconstruct symmetric rank- 1 matrices from inner products with subclasses of positive semidefinite matrices. For such subclasses, we introduce random cubatures for spaces of multivariate polynomials based on moment conditions. The inner products with samples from sufficiently strong random cubatures allow the reconstruction of symmetric rank- 1 matrices with a decent probability by solving the feasibility problem of a semidefinite program.

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1

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1

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Daty

otrzymano
2015-05-29
zaakceptowano
2015-10-06
online
2015-12-31

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autor
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Bibliografia

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  • [8] B. G. Bodmann and N. Hammen, Stable phase retrieval with low-redundancy frames, arXiv:1302.5487v1 (2013). [WoS]
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  • [11] J. Cahill, P. G. Casazza, J. Peterson, and L. Woodland, Phase retrieval by projections, arXiv:1305.6226v3 (2013).
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  • [18] M. Ehler, Random tight frames, J. Fourier Anal. Appl. 18 (2012), no. 1, 1–20. [Crossref]
  • [19] M. Ehler and M. Gräf, Cubatures and designs in unions of Grassmann spaces, arXiv (2014).
  • [20] M. Ehler and S. Kunis, Phase retrieval using time and Fourier magnitude measurements, 10th International Conference on Sampling Theory and Applications, 2013.
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  • [27] A. T. James, Distributions of matrix variates and latent roots derived from normal samples, Annals ofMathematical Statistics 35 (1964), no. 2, 475–501. [Crossref]
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  • [30] R. Kueng, H. Rauhut, and U. Terstiege, Low rank matrix recovery from rank one measurements, arXiv:1410.6913 (2014).
  • [31] H. N. Mhaskar, F. J. Narcowich, and J. D. Ward, Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature, Math. Comp. 70 (2002), 1113–1130. [Crossref]
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  • [33] F. Philipp, Phase retrieval from 4n-4 measurements: A proof for injectivity, Proc. Appl. Math. Mech. 14 (2014), no. 833-834. [Crossref]
  • [34] E. Riegler and G. Tauböck, Almost lossless analog compression without phase information, in Proc. IEEE Int. Symp. Inf. Th. (Hong Kong, China), 2015, pp. 1–5.
  • [35] T. Strohmer and R. W. Heath, Grassmannian frames with applications to coding and communication, Appl. Comput. Harmon. Anal. 14 (2003), no. 3, 257–275. [Crossref]
  • [36] J.A. Tropp, User-friendly tools for random matrices: An introduction., NIPS.
  • [37] J.A. Tropp„ User-friendly tail bounds for sums of random matrices, Journal Foundations of Computational Mathematics 12 (2012), no. 4, 389–434. [WoS]
  • [38] I. Waldspurger, A. d’Aspremont, and S. Mallat, Phase recovery, maxcut and complex semidefinite programming, arXiv:1206.0102v2 (2012).
  • [39] T. Wong, Generalized Dirichlet distribution in Bayesian analysis, Appl. Math. Comput. 97 (1998), no. 2-3, 165–181. [Crossref]

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_1515_wwfaa-2015-0005
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