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.