Our purpose in this section is to show the visual and quantitative evaluations of the developed nonconvex strategy for image inpainting. In conclusion, we end this article with some summative remarks in Section 5. Several experimental simulations and comparisons, which are detailed in Section 4, aim to demonstrate the outstanding performance of the proposed strategy. In Section 3, we minutely describe the process of deducing the designed optimization algorithm: primal-dual method. Section 2 is devoted to the overview of some basic mathematical preliminaries, and the proposal of a new nonconvex inpainting model. All numerical simulations consistently illustrate the superiority of the introduced method for image inpainting over the related efficient solvers, with respect to both visual and measurable comparisons.įinally, we give a briefly outline of the following sections. Secondly, to optimize the resulting nonconvex model, this paper presents in detail a modified primal-dual framework by combining the iteratively reweighted minimization algorithm. The usage of nonconvex penalizers in the TGV seminorm helps to obtain a more realistic image with sharp edges and no staircasing. First of all, we propose a novel nonconvex regularization model that closely integrates the superiorities of TGV regularizer and nonconvex logarithmic function. The main contributions of the current article are listed as follows. It is noteworthy that the concrete formulation will be detailed in the next section. Among these models, one of the remarkable variational solvers based on Rudin et al. ( 1992) is the TV inpainting model Moreover, considering inpainting in the transformed domain, the works (Chan et al., 2006, 2009) discussed the TV minimization wavelet domain models for image inpainting. The authors in Masnou and Morel ( 1998), Chan et al. ( 2002) investigated the Euler’s elastica and curvature based variational inpainting models. Subsequently, Chan and Shen ( 2001) developed a novel PDE model based on curvature driven diffusion, and the total variation (TV) model (Chan and Shen, 2002). Notice that the terminology of digital inpainting was initially introduced by Bertalmio et al. ( 2000), who proposed the typical third-order nonlinear PDE inpainting approach. For solving this inverse problem, there have emerged numerous models based on the variational, partial differential equation (PDE), wavelet, as well as Bayesian methods. The objective of image inpainting is to reconstruct the missing or damaged portions of image. As is well known to all, it has played a very significant role in the fields of artwork restoration, redundant target removal, image segmentation and video processing. The research of image inpainting is an important and challenging topic in image processing and computer vision. The data term E(x x0) E ( x x 0) is usually easy. Such problems are often formulated as an optimization task: min x E(x x0)+R(x), (1) (1) min x E ( x x 0) + R ( x), where E(x x0) E ( x x 0) is a data term and R(x) R ( x) is an image prior. In image restoration problems the goal is to recover original image x x having a corrupted image x0 x 0.There are especial cases: blurring due to incorrect focus and blurring due to movement - and these very defects, which each of you knows very well, and which are very difficult to correct - were selected as the subject of. Restoration of distorted images is one of the most interesting and important problems of image processing - from the theoretical, as well as from the practical point of view.
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