### Abstract

Original language | English (US) |
---|---|

Pages (from-to) | 15-22 |

Number of pages | 8 |

Journal | Contemporary mathematics |

Volume | 650 |

State | Published - 2015 |

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### Bibliographical note

Includes bibliographical references### Cite this

*Contemporary mathematics*,

*650*, 15-22.

**On Lipschitz Inversion of Nonlinear Redundant Representations.** / Balan, Radu; Zou, Dongmian.

Research output: Contribution to journal › Article

*Contemporary mathematics*, vol. 650, pp. 15-22.

}

TY - JOUR

T1 - On Lipschitz Inversion of Nonlinear Redundant Representations

AU - Balan, Radu

AU - Zou, Dongmian

N1 - Includes bibliographical references

PY - 2015

Y1 - 2015

N2 - In this note we show that reconstruction from magnitudes of frame coefficients (the so called “phase retrieval problem”) can be performed us-ing Lipschitz continuous maps. Specifically we show that when the nonlin-ear analysis map α: H → Rm is injective, with (α(x))k = |〈x, fk〉|2, where {f1, · · · , fm} is a frame for the Hilbert space H, then there exists a left inverse map ω: Rm → H that is Lipschitz continuous. Additionally we obtain that the Lipschitz constant of this inverse map is at most 12 divided by the lower Lipschitz constant of α. 1.

AB - In this note we show that reconstruction from magnitudes of frame coefficients (the so called “phase retrieval problem”) can be performed us-ing Lipschitz continuous maps. Specifically we show that when the nonlin-ear analysis map α: H → Rm is injective, with (α(x))k = |〈x, fk〉|2, where {f1, · · · , fm} is a frame for the Hilbert space H, then there exists a left inverse map ω: Rm → H that is Lipschitz continuous. Additionally we obtain that the Lipschitz constant of this inverse map is at most 12 divided by the lower Lipschitz constant of α. 1.

M3 - Article

VL - 650

SP - 15

EP - 22

JO - Contemporary mathematics

JF - Contemporary mathematics

ER -