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arXiv 1908.00801eess.IVcs.CVcs.NAmath.NA

Space-adaptive anisotropic bivariate Laplacian regularization for image restoration

CMAP, CNRS, École Polytechnique, Institut Polytechnique de Paris(巴黎综合理工学院综合理工学院应用数学中心、法国国家科学研究中心);University of Bologna(博洛尼亚大学)

Luca Calatroni, Alessandro Lanza, Monica Pragliola, Fiorella Sgallari

英文摘要:

In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anisotropic extension of the classical isotropic Total Variation (TV) regularizer. The proposed regularizer comes from the statistical assumption that the gradients of the target image distribute locally according to space-variant bivariate Laplacian distributions. The highly flexible variational structure of the corresponding regularizer encodes several free parameters which hold the potential for faithfully modelling the local geometry in the image and describing local orientation preferences. For an automatic estimation of such parameters, we design a robust maximum likelihood approach and report results on its reliability on synthetic data and natural images. A minimization algorithm based on the Alternating Direction Method of Multipliers (ADMM) is presented for the efficient numerical solution of the proposed variational model. Some experimental results are reported which demonstrate the high-quality of restorations achievable by the proposed model, in particular with respect to classical Total Variation regularization.

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