Saving phase: Injectivity and stability for phase retrieval
نویسندگان
چکیده
منابع مشابه
An algebraic characterization of injectivity in phase retrieval
A complex frame is a collection of vectors that span C and define measurements, called intensity measurements, on vectors in C . In purely mathematical terms, the problem of phase retrieval is to recover a complex vector from its intensity measurements, namely the modulus of its inner product with these frame vectors. We show that any vector is uniquely determined (up to a global phase factor) ...
متن کاملPhase Retrieval: Stability and Recovery Guarantees
Article history: Received 16 November 2012 Revised 31 July 2013 Accepted 17 August 2013 Available online xxxx Communicated by Bruno Torresani
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In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set F of m vectors in the complex Hilbert space of dimension n allows for vector reconstruction from magnitudes of its coefficients, then there is a perturbation bound ρ so that any frame set within ρ from F has the same property. In par...
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Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to recover the unknown signal – this is called phase retrieval. Phase retrieval has been a popular subject of research in the last few years, both in determining ...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2014
ISSN: 1063-5203
DOI: 10.1016/j.acha.2013.10.002