Wavelet transform and maximum entropy method
E. Pantin, Jean‐Luc Starck · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
In 1994, to overcome the difficulties encountered by the maximum entropy method (MEM) to restore images containing both high and low frequencies, Bonteoke et al. introduced the Pyramid Maximum Entropy Deconvolution. However, this method presents several drawbacks such as parameters estimation (model, alpha). Furthermore, in their method they don't minimize any functional. Following these ideas, we propose the multiresolution maximum entropy method which is based on the concept of multiscale entropy derived from the wavelet decomposition of a signal into different frequency bands. It leads to a method which is flux conservative, and the use of a multiresolution support solves the problem of MEM to choose the (alpha) parameter, i.e. relative weight between the goodness-of-fit and the entropy. We also show that our algorithm is efficient for filtering astronomical images.