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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

An Image Restoration Technique with Error Estimates   (Citations: 8)
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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 wavelet-like 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 model-based 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 X-ray source. Subject heading gs: methods: data analysis — techniques: high angular resolution
Journal: Astrophysical Journal - ASTROPHYS J , vol. 610, no. 2, pp. 1213-1227, 2004
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    • ...Our main contributions are: (1) Regarding the problem of image representation, besides the conventional separable binary-tree imagerepresentationinvolvingbeta-mixturerate-ratio densities, we explore a recursive quad-tree image representation, explicitly tailored to 2-D data, involving Dirichlet-mixture rate-ratio densities; a similar single-component Dirichlet quad-tree 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 single-component 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 single-component Dirichlet prior distribution...

    Stamatios Lefkimmiatiset 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 pixel-wise 3# limit...

    A. Connorset al. How To Win With Non-Gaussian Data: Poisson Goodness-of-Fit

    • ...(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. Whiteet 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. Highly-Structured Statistical Models in High-Energy Astrophysics

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