An Image Restoration Technique with Error Estimates

Abstract

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.

THECHANDRAHRC VIEW OF THE SUBARCSECOND STRUCTURES IN THE NUCLEAR REGION OF NGC 1068

“…Following our Chandra HRC study of the Seyfert 1 galaxy NGC 4151 (Wang et al 2009b), we performed image restoration using the expectation through Markov Chain Monte Carlo (EMC2) algorithm (Esch et al 2004;Karovska et al 2005). The effectiveness of this method was demonstrated with a number of astronomical imaging studies (Karovska et al 2005(Karovska et al , 2007Wang et al 2009b).…”

Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising

“…3) Interscale dependencies: Modeling interscale dependencies among intensity/rate ratios arising in natural images. Our main contributions are: (1) Regarding the problem of image representation, besides the conventional separable binary-tree image representation involving beta-mixture rate-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 deconvolution. Further, we propose a novel directional multiscale image representation, termed Poisson-Haar decomposition due to its close relation with the 2-D Haar wavelet transform, which better captures the edge detail structure of images, thus providing improved results in image modeling and consequently in the intensity estimation problem.…”

“…A similar decomposition scheme was first mentioned but not further pursued in [20]. 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.…”

“…Moreover in this case, as opposed to the separable and quad schemes there is a direct relation between the rateratios with the 2-D Haar wavelet detail coefficient in the corresponding subband, similarly to the 1-D case discussed in Section II-B In addition, is a re-scaled version of the 2-D Haar scaling coefficient . Equation (16) implies that we can employ an equivalent vector representation for the intensity image , as follows: (17) where the vectors are of the form:…”

CHEERS Results from NGC 3393. II. Investigating the Extended Narrow-line Region Using Deep Chandra Observations and Hubble Space Telescope Narrow-line Imaging

“…Koss et al (2015) note a general correspondence between O III and X-ray emission, as well as the expected role of the radio jets in shaping the ENLR, but here we examine the ENLR X-ray morphology in greater detail, examining the physical origin of ENLR substructure. Such inquiry is enabled by our use of EMC2 Bayesian deconvolution (Esch et al 2004;Karovska et al 2005Karovska et al , 2007 Fig. 1) with respect to the X-ray images, as well as our analysis of the S II images, which were not used by Cooke et al (2000) or Koss et al (2015).…”