Bayesian image reconstruction from partial image and aliased spectral intensity data

Baskaran, S.; Millane, Rick P.

doi:10.1109/83.791967

Cited by 3 publications

(3 citation statements)

References 31 publications

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“…The MAP estimate maximizes the posterior distribution, where the posterior distribution is defined as the product of the likelihood function and the prior distribution. Similar framework has been proposed for different phase retrieval problems [16,17].…”

Section: Spr Methodsmentioning

confidence: 99%

“…This combination is effective for the problem and is distinct from other Bayesian approaches proposed for different phase retrieval problems [16,17]. Compared to the widely used hybrid input-output (HIO) method [18][19][20], the SPR method does not require the support region and is robust against the limited photon counts and the missing central pixels.…”

Section: Introductionmentioning

confidence: 99%

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Phase retrieval from single biomolecule diffraction pattern

Ikeda¹,

Kono²

2012

Opt. Express

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In this paper, we propose the SPR (sparse phase retrieval) method, which is a new phase retrieval method for coherent x-ray diffraction imaging (CXDI). Conventional phase retrieval methods effectively solve the problem for high signal-to-noise ratio measurements, but would not be sufficient for single biomolecular imaging which is expected to be realized with femto-second x-ray free electron laser pulses. The SPR method is based on the Bayesian statistics. It does not need to set the object boundary constraint that is required by the commonly used hybrid input-output (HIO) method, instead a prior distribution is defined with an exponential distribution and used for the estimation. Simulation results demonstrate that the proposed method reconstructs the electron density under a noisy condition even some central pixels are masked.

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Section: Spr Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phase retrieval from single biomolecule diffraction pattern

Ikeda¹,

Kono²

2012

Opt. Express

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“…The observed intensity has to be decomposed into its components ®rst, followed by determining the phases for each. An approach based on Bayesian statistics has been suggested recently for this problem , 1998, 1999a, 1999b. Simulations show that its performance is superior to that of other techniques.…”

Section: Introductionmentioning

confidence: 99%

The likelihood function in fiber diffraction

Mu¹,

Makowski²

2000

Acta Cryst Sect A

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The likelihood function is an appropriate target function for re®nement of molecular structures using ®ber diffraction data. However, its practical application to ®ber diffraction faces two signi®cant obstacles: (i) the intensities of layer lines in a ®ber diffraction pattern usually arise from the superposition of several terms, each equivalent to a crystallographic structure factor, thereby making the calculation signi®cantly more complex than for the crystallographic case; (ii) to describe a molecular structure at the atomic level based on ®ber diffraction data, the radial and phase parts of the atomic coordinates must be treated separately owing to the uniaxial symmetry of the structure. These issues are addressed here in order to derive equations of likelihood functions for ®ber diffraction. The special case of a single term on a layer line is treated ®rst followed by extension of the method to the multiterm case. A practical dif®culty in implementation of likelihood for the multiterm case is that each term has a different variance. An analytical technique is described that allows the conversion of the unequal-variance case to an equal-variance case. This makes it possible to express the likelihood by an explicit formula, allowing a direct implementation of the likelihood calculation. A cylindrically symmetric model is proposed for error distribution of the atomic coordinates in a helical structure. Variances and offset coef®cients of the contributing terms in the likelihood functions are expressed in terms of the variance of the atomic coordinates in the cylindrical reference system.

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Image spectral amplitude distributions

Hsiao

Millane

2006

J. Opt. Soc. Am. A

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Models for the probability density functions of the Fourier amplitude of images are derived. The densities are based on a simple model of an image made up of independent objects and incorporates the observed behavior of the circularly averaged power spectrum versus spatial frequency. The density function over all spatial frequencies gives a good fit to spectral amplitude data from a variety of images.

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Bayesian image reconstruction from partial image and aliased spectral intensity data

Cited by 3 publications

References 31 publications

Phase retrieval from single biomolecule diffraction pattern

Phase retrieval from single biomolecule diffraction pattern

The likelihood function in fiber diffraction

Image spectral amplitude distributions

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