Maximum-entropy image reconstruction using wavelets

Abstract

The maximum-entropy method (MEM) is often used for enhancing astronomical images and, in particular, has recently been applied to cosmic microwave background (CMB) observations. Wavelet functions are also now used widely in astronomy, since they allow the sparse and efficient representation of a signal at different scales, and the application of wavelets to the denoising of CMB maps has been investigated. In this paper, we give a systematic discussion of how to combine these two approaches by the use of the MEM in wavelet bases for the denoising and deconvolution of general images and, in particular, CMB maps. We find that the MEM in the à trous wavelet basis 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 is 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.