A multi-parameter regularization model for image restoration

• Based on total variation and wavelet frame, a multi-parameter regularization model for image restoration is proposed.
• An effective algorithm based on ADMM is given for solving the new model, i.e., TVframe.
• Convergence analysis of the new algorithm is given.
• Numerical experiments show that TVframe outperforms several state-of-the-art image restoration approaches.

This paper presents a new multi-parameter regularization model for image restoration (IR) based on total variation (TV) and wavelet frame (WF). On one hand, the Rudin–Osher–Fatemi (ROF) model using TV as the regularization term has been proven to be very effective in preserving sharp edges and object boundaries which are usually the most important features to recover. On the other hand, adaptively exploiting the regularity of natural images has led to the successful WF approaches for IR. In this paper, we propose a novel model that combines these two approaches together to restore images from blurry, noisy and partial observations. Computationally, we use the alternative direction method of multiplier (ADMM) to solve the new model and provide its convergence analysis in the appendix. Numerical experiments on a set of IR benchmark problems show that the proposed model and algorithm outperform several state-of-the-art approaches in terms of the restoration quality.