Model bias in Bayesian image reconstruction from x-ray fiber diffraction data

Baskaran, S.; Millane, Rick P.

doi:10.1364/josaa.16.000236

Cited by 4 publications

(3 citation statements)

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“…Some of the spurious peaks, in fact, correspond to peaks in the known part of the image, (see Fig. 5), since the reconstructions are dominated by when there are fewer data This effect is referred to as "model bias" by crystallographers and is addressed in detail in a separate paper [28]. Referring to Fig.…”

Section: Image Reconstructionmentioning

confidence: 99%

Bayesian image reconstruction from partial image and aliased spectral intensity data

Baskaran

Millane

1999

IEEE Trans. on Image Process.

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Abstract-An image reconstruction problem motivated by xray fiber diffraction analysis is considered. The experimental data are sums of the squares of the amplitudes of particular sets of Fourier coefficients of the electron density, and a part of the electron density is known. The image reconstruction problem is to estimate the unknown part of the electron density, the "image." A Bayesian approach is taken in which a prior model for the image is based on the fact that it consists of atoms, i.e., the unknown electron density consists of separated, sharp peaks. Currently used heuristic methods are shown to correspond to certain maximum a posteriori estimates of the Fourier coefficients. An analytical solution for the Bayesian minimum mean-squareerror estimate is derived. Simulations show that the minimum mean-square-error estimate gives good results, even when there is considerable data loss, and out-performs the maximum a posteriori estimates.

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Section: Image Reconstructionmentioning

confidence: 99%

Bayesian image reconstruction from partial image and aliased spectral intensity data

Baskaran

Millane

1999

IEEE Trans. on Image Process.

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“…Expressed in terms of generalized hypergeometric functions in several variables, his formula converges impossibly slowly. The general unequalvariance case is also considered by Baskaran & Millane (1998).…”

Section: Likelihood For the Case Of Multiple Bessel Termsmentioning

confidence: 99%

“…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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Developments in fiber diffraction

Stubbs

1999

Current Opinion in Structural Biology

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Model bias in Bayesian image reconstruction from x-ray fiber diffraction data

Cited by 4 publications

References 10 publications

Bayesian image reconstruction from partial image and aliased spectral intensity data

Bayesian image reconstruction from partial image and aliased spectral intensity data

The likelihood function in fiber diffraction

Developments in fiber diffraction

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