Nonconvex Total Generalized Variation Model for Image Inpainting

Liu, Xinwu

doi:10.15388/20-INFOR438

Informatica

Nonconvex Total Generalized Variation Model for Image Inpainting

Volume 32, Issue 2 (2021), pp. 357–370

Xinwu Liu

https://doi.org/10.15388/20-INFOR438

Pub. online: 8 December 2020 Type: Research Article

Open Access

Received
1 May 2020

Accepted
1 November 2020

Published
8 December 2020

Abstract

It is a challenging task to prevent the staircase effect and simultaneously preserve sharp edges in image inpainting. For this purpose, we present a novel nonconvex extension model that closely incorporates the advantages of total generalized variation and edge-enhancing nonconvex penalties. This improvement contributes to achieve the more natural restoration that exhibits smooth transitions without penalizing fine details. To efficiently seek the optimal solution of the resulting variational model, we develop a fast primal-dual method by combining the iteratively reweighted algorithm. Several experimental results, with respect to visual effects and restoration accuracy, show the excellent image inpainting performance of our proposed strategy over the existing powerful competitors.

References

Bauss, F., Nikolova, M., Steidl, G. (2013). Fully smoothed ℓ1-TV models: bounds for the minimizers and parameter choice. Journal of Mathematical Imaging and Vision, 48(2), 295–307.

Bertalmio, M., Sapiro, G., Caselles, V., Ballester, C. (2000). Image inpainting. Computer Graphics, SIGGRAPH, 2000, 417–424.

Black, M.J., Rangarajan, A. (1996). On the unification of line processes, outlier rejection, and robust statistics with applications in early vision. International Journal of Computer Vision, 19(1), 57–91.

Bredies, K., Kunisch, K., Pock, T. (2010). Total generalized variation. SIAM Journal on Imaging Sciences, 3(3), 492–526.

Candès, E.J., Wakin, M.B., Boyd, S.P. (2008). Enhancing sparsity by reweighted ℓ1 minimization. Journal of Fourier Analysis and Applications, 14(5–6), 877–905.

Chambolle, A., Pock, T. (2011). A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, 40(1), 120–145.

Chan, T., Marquina, A., Mulet, P. (2000). High-order total variation-based image restoration. SIAM Journal on Scientific Computing, 22(2), 503–516.

Chan, T.F., Shen, J. (2001). Nontexture inpainting by curvature driven diffusion (CDD). Journal of Visual Communication and Image Representation, 12(4), 436–449.

Chan, T.F., Shen, J. (2002). Mathematical models for local nontexture inpaintings. SIAM Journal on Applied Mathematics, 62(3), 1019–1043.

Chan, T.F., Kang, S.H., Shen, J. (2002). Euler’s elastica and curvature-based inpainting. SIAM Journal on Applied Mathematics, 63(2), 564–592.

Chan, T.F., Shen, J., Zhou, H.M. (2006). Total variation wavelet inpainting. Journal of Mathematical Imaging and Vision, 25(1), 107–125.

Chan, R., Wen, Y., Yip, A. (2009). A fast optimization transfer algorithm for image inpainting in wavelet domains. IEEE Transactions on Image Processing, 18(7), 1467–1476.

Esser, E., Zhang, X., Chan, T. (2010). A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science. SIAM Journal on Imaging Sciences, 3(4), 1015–1046.

Gilboa, G., Osher, S. (2008). Nonlocal operators with applications to image processing. Multiscale Modeling and Simulation, 7(3), 1005–1028.

Knoll, F., Bredies, K., Pock, T., Stollberger, R. (2011). Second order total generalized variation (TGV) for MRI. Magnetic Resonance in Medicine, 65(2), 480–491.

Liu, X. (2018). A new TGV-Gabor model for cartoon-texture image decomposition. IEEE Signal Processing Letters, 25(8), 1221–1225.

Liu, X. (2019). Total generalized variation and shearlet transform based Poissonian image deconvolution. Multimedia Tools and Applications, 78(13), 18855–18868.

Liu, X., Huang, L. (2014). A new nonlocal total variation regularization algorithm for image denoising. Mathematics and Computers in Simulation, 97, 224–233.

Lysaker, M., Lundervold, A., Tai, X.-C. (2003). Noise removal using fourth order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Transactions on Image Processing, 12(12), 1579–1590.

Masnou, S., Morel, J.M. (1998). Level lines based disocclusion. In: Proceedings of IEEE International Conference on Image Processing (ICIP 98), Vol. 3, pp. 259–263.

Nikolova, M., Ng, M.K., Tam, C.-P. (2010). Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction. IEEE Transactions on Image Processing, 19(12), 3073–3088.

Nikolova, M., Ng, M.K., Tam, C.-P. (2013). On ℓ1 data fitting and concave regularization for image recovery. SIAM Journal on Scientific Computing, 35(1), A397–A430.

Ochs, P., Dosovitskiy, A., Brox, T., Pock, T. (2013). An iterated ℓ1 algorithm for non-smooth non-convex optimization in computer vision. In: IEEE Conference on Computer Vision and Pattern Recognition, Portland, OR, pp. 1759–1766.

Ochs, P., Dosovitskiy, A., Brox, T., Pock, T. (2015). On iteratively reweighted algorithms for nonsmooth nonconvex optimization. SIAM Journal on Imaging Sciences, 8(1), 331–372.

Prasath, V.B.S. (2017). Quantum noise removal in X-ray images with adaptive total variation regularization. Informatica, 28(3), 505–515.

Pratt, W.K. (2001). Digital Image Processing. 3rd ed. Jhon Wiley & Sons, New York.

Roth, S., Black, M.J. (2009). Fields of experts. International Journal of Computer Vision, 82(2), 205–229.

Rudin, L., Osher, S., Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D, 60(1–4), 259–268.

Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P. (2004). Image quality assessment: from error measurement to structural similarity. IEEE Transactions on Image Processing, 13(4), 600–612.

Zhang, L., Zhang, L., Mou, X., Zhang, D. (2011). FSIM: a feature similarity index for image qualtiy assessment. IEEE Transactions on Image Processing, 20(8), 2378–2386.

Zhang, H., Tang, L., Fang, Z., Xiang, C., Li, C. (2017). Nonconvex and nonsmooth total generalized variation model for image restoration. Signal Processing, 143(1), 69–85.

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Keywords

image inpainting nonconvex function total generalized variation primal-dual method

Funding

This work was supported by National Natural Science Foundation of China (61402166), Scientific Research Fund of Hunan Provincial Education Department (19B215) and Hunan Provincial Natural Science Foundation of China (2020JJ4285).

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