Deconvolution based on the curvelet transform

This paper describes a new deconvolution algorithm, based on both the wavelet transform and the curvelet transform. It extends previous results which were obtained for the denoising problem. Using these two different transformations in the same algorithm allows us to optimally detect in the same time isotropic features, well represented by the wavelet transform, and edges better represented by the curvelet transform. Adding a TV penalization term avoids the presence of oscillatory patterns around the edges which may appear when using multiscale methods. We illustrate the results with simulations.