Iterative Regularization and Nonlinear Inverse Scale Space in Curvelet-type Decomposition Spaces

In this paper we generalize the iterative regularization method and the inverse scale space method, recently developed for wavelet-based image restoration, to curvelet-type decomposition spaces setting. We obtain the result that minimzer of the new model can be derived as curvelet firm shrinkage with curvelet-type weight, which is dynamically changing in the iteration(CDS-IRM). And we obtain a new class of nonlinear inverse scale spaces flow which is dependent on Curvelet-type decomposition scale and smooth order(CDS-ISS). Numerical experiments indicate that the proposed methods are very efficient for denoising.