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Keywords
(11)
bayesian model
Data Analysis Techniques
Error Estimate
High Angular Resolution
Image Restoration
Markov Chain Monte Carlo
Multiscale Representation
Point Source
Smoothing Parameter
Subject Headings
Xray Source
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(1)
A statistical multiscale framework for Poisson inverse problems
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An Image Restoration Technique with Error Estimates
An Image Restoration Technique with Error Estimates,10.1086/421761,Astrophysical Journal,David N. Esch,Alanna Connors,Margarita Karovska,David A. van
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An Image Restoration Technique with Error Estimates
(
Citations: 8
)
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David N. Esch
,
Alanna Connors
,
Margarita Karovska
,
David A. van Dyk
Image restoration
including deconvolution techniques offers a powerful tool to improve resolution in images and to extract information on the multiscale structure stored in astronomical observations. We present a new method for statistical deconvolution, which we call expectation through
Markov Chain Monte Carlo
(EMC2). This method is designed to remedy several shortfalls of currently used deconvolution and restoration techniques for Poisson data. We use a waveletlike
multiscale representation
of the true image to achieve smoothing at all scales of resolution simultaneously, thus capturing detailed features in the image at the same time as larger scale extended features. Thus, this method smooths the image, while maintaining the ability to effectively reconstruct point sources and sharp features in the image. We use a principled, fully Bayesian modelbased analysis, which produces extensive information about the uncertainty in the fitted smooth image, allowing assessment of the errors in the resulting reconstruction. Our method also includes automatic fitting of the multiscale smoothing parameters. We show several examples of application of EMC2 to both simulated data and a real astronomical Xray source. Subject heading gs: methods:
data analysis
— techniques:
high angular resolution
Journal:
Astrophysical Journal  ASTROPHYS J
, vol. 610, no. 2, pp. 12131227, 2004
DOI:
10.1086/421761
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Citation Context
(4)
...Our main contributions are: (1) Regarding the problem of image representation, besides the conventional separable binarytree imagerepresentationinvolvingbetamixturerateratio densities, we explore a recursive quadtree image representation, explicitly tailored to 2D data, involving Dirichletmixture rateratio densities; a similar singlecomponent Dirichlet quadtree image representation was first studied by [
17
] in the context of image ...
...Later, it was studied in [
17
] in the context of image deblurring; however, the authors in [17] only considered the simpler case of a singlecomponent Dirichlet prior distribution...
...Later, it was studied in [17] in the context of image deblurring; however, the authors in [
17
] only considered the simpler case of a singlecomponent Dirichlet prior distribution...
Stamatios Lefkimmiatis
,
et al.
Bayesian Inference on Multiscale Models for Poisson Intensity Estimati...
...In order to fully map out the posterior distribution of the various model and tuning parameters,
Esch et al. (2004)
uses a Markov Chain Monte Carlo sampler...
...We emphasize that although we are not discussing it here, NK and EMC2 do have the capacity to “deconvolve” the image, see
Esch et al. (2004)
and Karovska et al. (2005)...
...Even the first uses of EMC2 followed (roughly) this usual thinking (
Esch et al. 2004;
Karovska et al. 2005), defining the boundary at the pixelwise 3# limit...
A. Connors
,
et al.
How To Win With NonGaussian Data: Poisson GoodnessofFit
...(1999), Nowak and Kolaczyk (2000), and
Esch et al. (2004)
...
...(1999) and
Esch et al. (2004)
, is given by factoring this simple statistical model...
...We agree with
Esch et al. (2004)
that the mean of the...
...
Esch et al. (2004)
also introduce the use of signiflcance maps that use the...
John T. White
,
et al.
Bayesian Poisson Image Smoothing using a Chinese Restaurant Process wi...
...cussed in van Dyk and Hans [2002] and
Esch et al. [2004]
...
David A. van Dyk
.
HighlyStructured Statistical Models in HighEnergy Astrophysics
References
(1)
Astronomical image and data analysis
(
Citations: 93
)
JeanLuc Starck
,
Fionn Murtagh
Published in 2002.
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Citations
(8)
Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to PhotonLimited Image Denoising
(
Citations: 6
)
Stamatios Lefkimmiatis
,
Petros Maragos
,
George Papandreou
Journal:
IEEE Transactions on Image Processing
, vol. 18, no. 8, pp. 17241741, 2009
Multiscale Analysis of PhotonLimited Astronomical Images
(
Citations: 8
)
Rebecca Willett
Published in 2007.
How To Win With NonGaussian Data: Poisson GoodnessofFit
A. Connors
,
D. A. van Dyk
Published in 2007.
Deconvolution in highenergy astrophysics: science, instrumentation, and methods
(
Citations: 4
)
David A. van Dyk
,
Alanna Connors
,
David N. Esch
,
Peter Freeman
,
Hosung Kang
,
Margarita Karovskak
,
Vinay Kashyap
,
Aneta Siemiginowskayy
,
Andreas Zezaszz
Published in 2006.
Astrophysics in 2004
(
Citations: 1
)
Virginia Trimble
,
Markus Aschwanden
Journal:
Publications of The Astronomical Society of The Pacific  PUBL ASTRON SOC PAC
, vol. 117, no. 830, pp. 311394, 2005