Filtering and deconvolution by the wavelet transform

The wavelet transform gives information in both spatial and frequency domains and is a very useful tool for describing the hierarchical structures. A new approach for filtering based on the wavelet transform is presented in this paper, and several algorithms are proposed. A criterion of quality, which takes into account the resolution, is used to compare these algorithms. We show that deconvolution can be done using filtered wavelet coefficients. By computing the wavelet from the point spread function, we find a new transform algorithm and a reconstruction method related to it.