Deconvolution of astronomical images using the multiscale maximum entropy method

Following the ideas of Bontekoe et al. who noticed that the classical Maximum Entropy Method (MEM) had difficulties to efficiently restore high and low spatial frequency structure in an image at the same time, we use the wavelet transform, a mathematical tool to decompose a signal into different frequency bands. We introduce the concept of multi-scale entropy of an image, leading to a better restoration at all spatial frequencies. This deconvolution method is flux conservative and the use of a multiresolution support solves the problem of MEM to choose the a parameter, i.e. the relative weight between the goodness-of-fit and the entropy. We show that our algorithm is efficient too for filtering astronomical images. A range of practical examples illustrate this approach.