Maximum-entropy image reconstruction using wavelets

Abstract

Wavelet functions allow the sparse and efficient representation of a signal at different scales. Recently the application of wavelets to the denoising of maps of cosmic microwave background (CMB) fluctuations has been proposed. The maximum-entropy method (MEM) is also often used for enhancing astronomical images and has been applied to CMB data. In this paper, we give a systematic discussion of combining these two approaches by the use of the MEM in wavelet bases for the denoising and deconvolution of CMB maps and more general images. Certain types of wavelet transforms, such as the a trous transform, can be viewed as a multi-channel intrinsic correlation function (ICF). We find that the wavelet MEM has lower reconstruction residuals than conventional pixel-basis MEM in the case when the signal-to-noise ratio is low and the point spread function narrow. Furthermore, the Bayesian evidence for the wavelet MEM reconstructions is generally higher for a wide range of images. From a Bayesian point of view, the wavelet basis thus provides a better model of the image.

21 pages, 20 figures, submitted to MNRAS

References in corpus (12)

• Foreground separation methods for satellite observations of the cosmic microwave background
• Isotropic Wavelets: a Powerful Tool to Extract Point Sources from CMB Maps
• A maximum-entropy method for reconstructing the projected mass distribution of gravitational lenses
• Maximum-entropy weak lens reconstruction: improved methods and application to data
• Wavelet analysis and the detection of non-Gaussianity in the CMB
• All-sky component separation for the Planck mission
• The entropic prior for distributions with positive and negative values
• Applications of Wavelets to the Analysis of Cosmic Microwave Background Maps
• Combining maximum-entropy and the mexican hat wavelet to reconstruct the microwave sky
• Wavelets Applied to CMB Maps: a Multiresolution Analysis for Denoising
• Analysis of CMB maps with 2D wavelets
• Separation of foregrounds from cosmic microwave background observations with the MAP satellite

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