A fast higher degree total variation minimization method for image restoration

Abstract

Based on the spectral decomposition theory, this paper presents a unified analysis of higher degree total variation (HDTV) model for image restoration. Under this framework, HDTV is reinterpreted as a family of weighted L₁–L₂ mixed norms of image derivatives. Due to the equivalent formulation of HDTV, we construct a modified functional for HDTV-based image restoration. Then, the minimization of the modified functional can be decoupled into two separate sub-problems, which correspond to the deblurring and denoising. Thus, we design a fast and efficient image restoration algorithm using an iterative Wiener deconvolution with fast projected gradient denoising (IWD-FPGD) scheme. Moreover, we show the convergence of the proposed IWD-FPGD algorithm for the special case of second-degree total variation. Finally, the systematic performance comparisons of the proposed IWD-FPGD algorithm demonstrate the effectiveness in terms of peak signal-to-noise ratio, structural similarity and convergence rate.

Keywords:

• higher degree total variation (HDTV)
• image restoration
• iterative Wiener deconvolution
• fast projected gradient denoising
• convergence

2010 AMS Subject Classifications:

• 65F10
• 65F22
• 65K10
• 68U10
• 94A08

Acknowledgements

The authors would like to thank the anonymous reviewers for their careful reading and useful comments on this paper.

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the Fundamental Research Funds for the Central Universities (30915012204), the National Nature Science Foundation of China (61171165 and 11431015), Nature Science Foundation of Jiangsu Province (BK2012800), National Scientific Equipment Developing Project of China (2012YQ050250) and Six Top Talents Project of Jiangsu Province (2012DZXX-036).