Image denoising using combined higher order non-convex total variation with overlapping group sparsity
- 216 Downloads
It is widely known that the total variation image restoration suffers from the stair casing artifacts which results in blocky restored images. In this paper, we address this problem by proposing a combined non-convex higher order total variation with overlapping group sparse regularizer. The hybrid scheme of both the overlapping group sparse and the non-convex higher order total variation for blocky artifact removal is complementary. The overlapping group sparse term tends to smoothen out blockiness in the restored image more globally, while the non-convex higher order term tends to smoothen parts that are more local to texture while preserving sharp edges. To solve the proposed image restoration model, we develop an iteratively re-weighted \(\ell _1\) based alternating direction method of multipliers algorithm to deal with the constraints and subproblems. In this study, the images are degraded with different levels of Gaussian noise. A comparative analysis of the proposed method with the overlapping group sparse total variation, the Lysaker, Lundervold and Tai model, the total generalized variation and the non-convex higher order total variation, was carried out for image denoising. The results in terms of peak signal-to-noise ratio and structure similarity index measure show that the proposed method gave better performance than the compared algorithms.
KeywordsAlternating direction method Total variation Denoising Non-convex Overlapping group sparsity
We would like to thank the anonymous reviewers for their valuable suggestions for improving this paper. We would also like to thank Dr. Jun Liu of University of Electronic Science and Technology of China for generously sharing the codes for OGSTV with us.
- Chartrand, R. (2007). Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Processing Letters, 14(10), 707–710.Google Scholar
- Condat, L. (2014). A generic proximal algorithm for convex optimization-application to total variation minimization. IEEE Signal Processing Letters, 21(8), 985–989.Google Scholar
- Figueiredo, M., Dias, J. B., Oliveira, J. P., Nowak, R. D., et al. (2006). On total variation denoising: A new majorization-minimization algorithm and an experimental comparison with wavalet denoising. In IEEE international conference on image processing (pp. 2633–2636), IEEE.Google Scholar
- Gong, P., Zhang, C., Lu, Z., Huang, J. Z., & Ye, J. (2013). A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems. In Proceedings of the international conference on machine learning (Vol. 28, p. 37), NIH Public Access.Google Scholar
- He, C., Hu, C., Yang, X., He, H., & Zhang, Q. (2014). An adaptive total generalized variation model with augmented Lagrangian method for image denoising. Mathematical Problems in Engineering, 2014, 11.Google Scholar
- Liu, R. W., Wu, D., Wu, C. S., Xu, T., & Xiong, N. (2015b). Constrained nonconvex hybrid variational model for edge-preserving image restoration. In IEEE international conference on systems, man, and cybernetics (pp 1809–1814).Google Scholar
- Liu, X. (2016). Weighted total generalised variation scheme for image restoration. Image Processing, IET, 10(1), 80–88.Google Scholar
- Lyu, Q., Lin, Z., She, Y., & Zhang, C. (2013). A comparison of typical \(\ell _p\) minimization algorithms. Neurocomputing, 119, 413–424.Google Scholar
- Papafitsoros, K. (2015). Novel higher order regularisation methods for image reconstruction. Ph.D. thesis, University of Cambridge.Google Scholar
- Parekh, A., & Selesnick, I. (2015). Convex denoising using non-convex tight frame regularization. IEEE Signal Processing Letters, 22(10), 1786–1790.Google Scholar
- Peyré, G., & Fadili, J. (2011). Group sparsity with overlapping partition functions. In Signal Processing Conference, 2011 19th European (pp 303–307), IEEE.Google Scholar
- Powell, M. J. D. (1969). A method for nonlinear constraints in minimization problems. In R. Fletcher (Ed.), Optimization (pp. 283–298). New York: Academic Press.Google Scholar
- Selesnick, I. W., & Chen, P. Y. (2013). Total variation denoising with overlapping group sparsity. In IEEE international conference on acoustics, speech and signal processing (ICASSP) (pp. 5696–5700), IEEE.Google Scholar
- Shi, M., Han, T., & Liu, S. (2016). Total variation image restoration using hyper-laplacian prior with overlapping group sparsity. Signal Processing, 126, 65–76.Google Scholar
- Tai, X. C., & Wu, C. (2009). Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model. In Scale space and variational methods in computer vision (pp 502–513), Springer.Google Scholar
- Tao, M., Yang, J., & He, B. (2009). Alternating direction algorithms for total variation deconvolution in image reconstruction. Research report, Rice University.Google Scholar
- Wang, Y., Yin, W., & Zeng, J. (2015). Global convergence of ADMM in nonconvex nonsmooth optimization. arXiv preprint arXiv:1511.06324.
- Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600–612.Google Scholar
- Zhang, Y. (2010). An alternating direction algorithm for nonnegative matrix factorization. preprint.Google Scholar