Abstract
In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anistropic extension of the classical Total Variation (TV) regularizer. The proposed regularizer comes from the statistical assumption that the gradients of the unknown target image distribute locally according to space-variant bivariate Laplacian distributions. The high flexibility of the proposed regularizer holds the potential for the effective modelling of local image properties, in particular driving in an adaptive manner the strength and the directionality of non-linear TV-diffusion. The free parameters of the regularizer are automatically set - and, eventually, updated - based on a robust Maximumum Likelihood estimation procedure. A minimization algorithm based on the Alternating Direction Method of Multipliers is presented for the efficient numerical solution of the proposed variational model. Some experimental results are reported. They demonstrate the high-quality of restorations achievable by the proposed model, in particular with respect to classical TV-regularized models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3, 1–122 (2011)
Calatroni, L., Lanza, A., Pragliola, M., Sgallari, F.: A flexible space-variant anisotropic regularization for image restoration with automated parameter selection. SIAM J. Imaging Sci. 12, 1001–1037 (2019)
Calatroni, L., Lanza, A., Pragliola, M., Sgallari, F.: Adaptive parameter selection for weighted-TV image reconstruction problems. J. Phys.: Conf. Ser. NCMIP 2019 (2019, to appear)
He, C., Hu, C., Zhang, W., Shi, B.: A fast adaptive parameter estimation for total variation image restoration. IEEE Trans. Image Process. 23, 4954–4967 (2014)
Lanza, A., Morigi, S., Pragliola, M., Sgallari, F.: Space-variant generalised Gaussian regularisation for image restoration. Comput. Methods Biomech. Biomed. Eng.: Imaging Vis., 1–14 (2018). https://doi.org/10.1080/21681163.2018.1471620
Lanza, A., Morigi, S., Pragliola, M., Sgallari, F.: Space-variant TV regularization for image restoration. In: Tavares, J.M.R.S., Natal Jorge, R.M. (eds.) VipIMAGE 2017. LNCVB, vol. 27, pp. 160–169. Springer, Cham (2018)
Lanza, A., Morigi, S., Sgallari, F.: Constrained TV\(_p\)-\(\ell _2\) model for image restoration. J. Sci. Comput. 68, 64–91 (2016)
Lanza, A., Morigi, S., Sgallari, F., Wen, Y.W.: Image restoration with Poisson-Gaussian mixed noise. Comput. Methods Biomech. Biomed. Eng.: Imaging Vis. 2, 12–24 (2014)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D: Nonlinear Phenom. 60, 259–268 (1992)
Stuart, A.M.: Inverse problems: a Bayesian perspective. Acta Numerica 19, 451–559 (2010)
Zhou, W., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 600–612 (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Calatroni, L., Lanza, A., Pragliola, M., Sgallari, F. (2019). Space-Adaptive Anisotropic Bivariate Laplacian Regularization for Image Restoration. In: Tavares, J., Natal Jorge, R. (eds) VipIMAGE 2019. VipIMAGE 2019. Lecture Notes in Computational Vision and Biomechanics, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-32040-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-32040-9_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32039-3
Online ISBN: 978-3-030-32040-9
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)