Controlled total variation regularization for image deconvolution

Abstract

To resolve the image deconvolution problem, the total variation (TV) minimization approach has been proved to be very efficient. However, we observe that this approach has an over-minimizing TV effect in the sense that it gives a solution whose TV is usually smaller than that of the original image. This effect is due to the pre-pondering role of the TV in the corresponding minimization problem and prevents from finding the exact solution of the deconvolution problem when such a solution exists. We propose a modified version of the gradient descent algorithm, which leads to an exact solution of the deconvolution problem if it exists and to a satisfactory approximative solution if there is no exact one. The idea consists in introducing a control on the contribution of the TV in the classical gradient descent algorithm. The new algorithm has the advantage that the restored image has the TV closer to that of the original image, compared to the classical gradient descent approach. Numerical results show that our method is competitive compared to some recent ones.

Keywords:

• Inverse problem
• Deconvolution
• Total variation
• Denoising

Acknowledgments

The authors are grateful to the reviewers for their valuable comments and remarks which helped to improve the paper. The work has been partially supported by the National Natural Science Foundation of China, grants no. 11571052 and no. 11401590.

Notes

* http://www.pami.sjtu.edu.cn/people/jinqy/index.files/Softwares/AlgorithmCTVandDGD.zip