Image Restoration by Second-Order Total Generalized Variation and Wavelet Frame Regularization

Jianguang Zhu,Binbin Hao,Kai Li

doi:10.1155/2019/3650128

Abstract

It has been proved that total generalized variation (TGV) can better preserve edges while suppressing staircase effect. In this paper, we propose an effective hybrid regularization model based on second-order TGV and wavelet frame. The proposed model inherits the advantages of TGV regularization and wavelet frame regularization, can eliminate staircase effect while protecting the sharp edge, and simultaneously has good capability of sparsely estimating the piecewise smooth functions. The alternative direction method of multiplier (ADMM) is employed to solve the new model. Numerical results show that our proposed model can preserve more details and get higher image visual quality than some current state-of-the-art methods.

Highlights

We propose an effective hybrid regularization model based on second-order total generalized variation (TGV) and wavelet frame
Image restoration refers to the problem of recovering image that satisfies people’s needs from an observed image that degraded by different blur and noise
We focus on the total generalized variation regularization which can be seen as a generalization of total variation

Summary

Introduction

Image restoration refers to the problem of recovering image that satisfies people’s needs from an observed image that degraded by different blur and noise. One of the most effective ways to deal with this problem is adding some regularized terms to objective function This leads to the following restoration model: muin. It is worth noticing that TGV involves and balances higherorder derivatives of u This results in the fact that the reconstruction by using TGV regularization can preserve edges while suppressing staircase effect. Numerical experiments show that the models based on wavelet frame and variational methods can significantly improve the quality of images [50, 51]. Owing to the proposed model making good use of the advantages of wavelet frame and total generalized variation regularization, the new proposed model can protect the sharp edges of the images, and make good use of the sparse prior information.

Review of Total Generalized Variation and the Wavelet Frame

The Proposed Model and Algorithm

Numerical Experiments

Findings

Conclusion