  Variational regularization models are one of the popular and efficient
approaches for image restoration. The regularization functional in the model
carries prior knowledge about the image to be restored. The prior knowledge, in
particular for natural images, are the first-order (i.e. variance in luminance)
and second-order (i.e. contrast and texture) information. In this paper, we
propose a model for image restoration, using a multilevel non-stationary tight
framelet system that can capture the image's first-order and second-order
information. We develop an algorithm to solve the proposed model and the
numerical experiments show that the model is effective and efficient as
compared to other higher-order models.
