A Multi-parameter Regularization Model for Deblurring Images Corrupted by Impulsive Noise

Abstract

This article considers image deblurring in the presence of impulse noise and proposes a new multi-parameter regularization model for image deblurring based on total variation (TV) and wavelet frame (WF), along with an efficient and effective solving algorithm for this restoring model. On the one hand, it is well known that the TV regularization-based Rudin–Osher–Fatemi model is very effective in preserving sharp edges and object boundaries which are generally the most important features to recover. On the other hand, WF-based approaches for image restoration have proven to be very successful in adaptively exploiting the regularity of natural images. By combining TV regularization and WF regularization, a novel multi-parameter regularization model is proposed for deblurring images in the presence of impulse noise. Numerically, the alternative direction method of multiplier (ADMM) with an adaptive scheme for choosing regularization parameters is provided and applied to this multi-parameter regularization model. Moreover, the convergence analysis of the ADMM is shown in the “Appendix.” Furthermore, numerical experiments involving images corrupted by various types of blurring kernels and different levels of noises indicate that the proposed model and algorithm outperform several state-of-the-art approaches in terms of the restoration quality, especially the ability to mitigate staircasing effects while preserving important features in images.