&lt;title&gt;Bayesian image reconstruction from partial image and spectral amplitude data&lt;/title&gt;

Baskaran, S.; Millane, Rick P.

doi:10.1117/12.292824

Cited by 4 publications

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“…The MAP2 structure factor estimates are therefore given by (41) and referring to (13) we see that Note that these two estimates maximize posterior densities for the Fourier coefficients, not the electron density.…”

Section: A Currently Used Methodsmentioning

confidence: 99%

“…Simulations are used to assess the performance of the MMSE estimate, and show its superiority over the MAP estimates. A preliminary account of this work has been reported [13].…”

Section: Introductionmentioning

confidence: 99%

“…In the second method, the estimates of denoted by are chosen so that the are all equal, and the phase of is equal to the phase of This gives (13) where denotes the number of elements in a set. Both methods have disadvantages.…”

Section: Introductionmentioning

confidence: 99%

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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: A Currently Used Methodsmentioning

confidence: 99%

“…Simulations are used to assess the performance of the MMSE estimate, and show its superiority over the MAP estimates. A preliminary account of this work has been reported [13].…”

Section: Introductionmentioning

confidence: 99%

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Bayesian image reconstruction from partial image and aliased spectral intensity data

Baskaran

Millane

1999

IEEE Trans. on Image Process.

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An improved prior for image reconstruction in X-ray fiber diffraction

Baskaran

Millane²

Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269)

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The structure completion problem in fiber diffraction is addressed from a Bayesian perspective. The experimental data are sums of the squares of the amplitudes of particular sets of Fourier coefficients of the electron density. In addition, a part of the electron density is known. The image reconstruction problem is to estimate the missing part of the electron density. A Bayesian approach is taken in which the 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. The conventional prior assumes that the positions of the unknown atoms are uniformly distributed. We improve this prior by treating the positions of the known atoms as containing normally distributed coordinate errors. 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 better results when the new prior is used.

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<title>Bayesian image reconstruction with a hyperellipsoidal posterior in x-ray fiber diffraction</title>

Baskaran

Millane²

1998

SPIE Proceedings

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<title>Bayesian image reconstruction from partial image and spectral amplitude data</title>

Cited by 4 publications

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Bayesian image reconstruction from partial image and aliased spectral intensity data

Bayesian image reconstruction from partial image and aliased spectral intensity data

An improved prior for image reconstruction in X-ray fiber diffraction

<title>Bayesian image reconstruction with a hyperellipsoidal posterior in x-ray fiber diffraction</title>

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