Projections and phase retrieval
نویسندگان
چکیده
منابع مشابه
Norm Retrieval and Phase Retrieval by Projections
We make a detailed study of norm retrieval. We give several classification theorems for norm retrieval and give a large number of examples to go with the theory. One consequence is a new result about Parseval frames: If a Parseval frame is divided into two subsets with spans W1, W2 and W1 ∩W2 = {0}, then W1 ⊥W2.
متن کاملPhase retrieval by iterated projections.
Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and three real parameters. For the standard application in optics, where the two projections implement Fourier modulus and object support constraints, respectively, the difference map reproduces the "hybrid" form of Fienup's input-output map when a particular choi...
متن کاملPhase retrieval with Fourier-weighted projections.
In coherent lensless imaging, the presence of image sidelobes, which arise as a natural consequence of the finite nature of the detector array, was early recognized as a convergence issue for phase retrieval algorithms that rely on an object support constraint. To mitigate the problem of truncated far-field measurement, a controlled analytic continuation by means of an iterative transform algor...
متن کاملRandom projections and the optimization of an algorithm for phase retrieval
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule. For a general class of algorithms, where the basic iteration is specified by the difference map, solutions are associated with fixed points of the map, the att...
متن کاملPhase retrieval and norm retrieval
Phase retrieval has become a very active area of research. We will classify when phase retrieval by Parseval frames passes to the Naimark complement and when phase retrieval by projections passes to the orthogonal complements. We introduce a new concept we call norm retrieval and show that this is what is necessary for passing phase retrieval to complements. This leads to a detailed study of no...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2017
ISSN: 1063-5203
DOI: 10.1016/j.acha.2015.12.004