منابع مشابه
Fourier Phase Retrieval: Uniqueness and Algorithms
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and algorithmic challenges. In general, there is no unique mapping between a one-dimensional signal and its Fourier magnitude and therefore the problem is ill-posed. Add...
متن کاملPhase Retrieval for Sparse Signals: Uniqueness Conditions
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from the magnitude of its Fourier transform to enable the reconstruction of the original signal. A fundamental question then is: “Under which conditions can we uniq...
متن کاملUniqueness transition in noisy phase retrieval
Previous criteria for the feasibility of reconstructing phase information from intensity measurements, both in x-ray crystallography and more recently in coherent x-ray imaging, have been based on the Maxwell constraint counting principle. We propose a new criterion, based on Shannon’s mutual information, that is better suited for noisy data or contrast that has strong priors not well modeled b...
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
متن کاملNumerical investigation of the uniqueness of phase retrieval
Both a new iterative grid-search technique and the iterative Fourier-transform algorithm are used to illuminate the relationships among the ambiguous images nearest a given object, error metric minima, and stagnation points of phase-retrieval algorithms. Analytic expressions for the subspace of ambiguous solutions to the phase-retrieval problem are derived for 2 X 2 and 3 X 2 objects. Monte Car...
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ژورنال
عنوان ژورنال: SIAM Review
سال: 2020
ISSN: 0036-1445,1095-7200
DOI: 10.1137/19m1256865