Phase-retrieval error: a lower bound

Cederquist, Jack N.; Wackerman, C.

doi:10.1364/josaa.4.001788

Cited by 26 publications

(15 citation statements)

References 2 publications

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“…Mutual information is an information-theoretic measure of the degree of correlation of two random variables 6 and in this case is written as I (K , W ). The mutual information is the difference of two entropies…”

Section: Capacity Of the Poisson Channelmentioning

confidence: 99%

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Effects of Adsorption and Thermal Desorption of Atomic Hydrogen on Electronic and Atomic Structures of Si(111)(√3×√3)-Al Surface

Li¹,

Hasegawa

Nakashima

1992

Jpn. J. Appl. Phys.

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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 by continuous variables. A natural application is magnetic domain imaging, where the criterion for uniqueness in the reconstruction takes the form that the number of photons, per pixel of contrast in the image, exceeds a certain minimum. Through detailed studies of a simple model, we develop an analogy between reconstruction uniqueness and the phases of a spin glass.

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Section: Capacity Of the Poisson Channelmentioning

confidence: 99%

“…the mutual information of the FPC can be directly related to the capacity of the simple Poisson channel (6). The discrete Fourier transform of x, written asx, is a linear transformation of x with the propertyx ·x * = x · x.…”

Section: The Fourier-poisson Channel (Fpc)mentioning

confidence: 99%

Effects of Adsorption and Thermal Desorption of Atomic Hydrogen on Electronic and Atomic Structures of Si(111)(√3×√3)-Al Surface

Li¹,

Hasegawa

Nakashima

1992

Jpn. J. Appl. Phys.

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“…To motivate our proposed model selection criterion, note that assuming a support , the length of the residual vectors is and in particular decreases with . Moreover, according to Lemma 2,when and are evaluated with the correct phase vector , at low noise levels, (19) Similar to other model selection criteria, we construct a functional with a data fit term and a penalty term with a penalty factor , (20) Our proposed is then (21) The penalty term in (20) depends on the constant . In light of (19), should be at least 1.…”

Section: B Estimating the Support Sizementioning

confidence: 99%

“…Moreover, according to Lemma 2,when and are evaluated with the correct phase vector , at low noise levels, (19) Similar to other model selection criteria, we construct a functional with a data fit term and a penalty term with a penalty factor , (20) Our proposed is then (21) The penalty term in (20) depends on the constant . In light of (19), should be at least 1. In our simulations we used , though our recovered is quite robust to the exact value of .…”

Section: B Estimating the Support Sizementioning

confidence: 99%

“…The former are limited by the size of the images, whereas the latter by efficiency and convergence [18]. Moreover, due to the non-convexity of the classical phase retrieval problem, relatively little is understood about the convergence or robustness to measurement noise of current algorithms [2], [19]. For a review of phase retrieval, we refer the reader to [1], [18], [20], [21] and references therein.…”

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confidence: 99%

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Vectorial Phase Retrieval of 1-D Signals

Raz

Dudovich

Nadler

2013

IEEE Trans. Signal Process.

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Abstract-Reconstruction of signals from measurements of their spectral intensities, also known as the phase retrieval problem, is of fundamental importance in many scientific fields. In this paper we present a novel framework, denoted as vectorial phase retrieval, for reconstruction of pairs of signals from spectral intensity measurements of the two signals and of their interference. We show that this new framework can alleviate some of the theoretical and computational challenges associated with classical phase retrieval from a single signal. First, we prove that for compactly supported signals, in the absence of measurement noise, this new setup admits a unique solution. Next, we present a statistical analysis of vectorial phase retrieval and derive a computationally efficient algorithm to solve it. Finally, we illustrate via simulations, that our algorithm can accurately reconstruct signals even at considerable noise levels.Index Terms-Convex relaxation, 1-D phase retrieval, signal recovery from modulus Fourier measurements, statistical model selection.

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Uniqueness transition in noisy phase retrieval

Elser

Eisebitt

2011

New J. Phys.

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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 by continuous variables. A natural application is magnetic domain imaging, where the criterion for uniqueness in the reconstruction takes the form that the number of photons, per pixel of contrast in the image, exceeds a certain minimum. Detailed studies of a simple model show that the uniqueness transition is of the type exhibited by spin glasses.

show abstract

Phase-retrieval error: a lower bound

Cited by 26 publications

References 2 publications

Effects of Adsorption and Thermal Desorption of Atomic Hydrogen on Electronic and Atomic Structures of Si(111)(√3×√3)-Al Surface

Effects of Adsorption and Thermal Desorption of Atomic Hydrogen on Electronic and Atomic Structures of Si(111)(√3×√3)-Al Surface

Vectorial Phase Retrieval of 1-D Signals

Uniqueness transition in noisy phase retrieval

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