A Universal Variational Framework for Sparsity-Based Image Inpainting

Abstract

In this paper, we extend an existing universal variational framework for image inpainting with new numerical algorithms. Given certain regularization operator Φ and denoting u the latent image, the basic model is to minimize the l(p), (p=0,1) norm of Φu preserving the pixel values outside the inpainting region. Utilizing the operator splitting technique, the original problem can be approximated by a new problem with extra variable. With the alternating minimization method, the new problem can be decomposed as two subproblems with exact solutions. There are many choices for Φ in our approach such as gradient operator, wavelet transform, framelet transform, or other tight frames. Moreover, with slight modification, we can decouple our framework into two relatively independent parts: 1) denoising and 2) linear combination. Therefore, we can take any denoising method, including BM3D filter in the denoising step. The numerical experiments on various image inpainting tasks, such as scratch and text removal, randomly missing pixel filling, and block completion, clearly demonstrate the super performance of the proposed methods. Furthermore, the theoretical convergence of the proposed algorithms is proved.

Learning Quadrangulated Patches for 3D Shape Parameterization and Completion

“…These non local algorithms can be categorised into dictionary based [8], [9], [10] and BM3D (Block-matching and 3D filtering) based [11], [12], [13] methods. Because of the presence of a block matching step in BM3D (patches are matched and kept in a block if they are similar), it is not simple to extend it for the task of inpainting, though the algorithm can be applied indirectly in a different domain [45]. In contrast, dictionary based methods can be extended for the problem of inpatinting by introducing missing data masks in the matrix factorization step (Right) Patches computed at multiple offset from the quad centres to simulate dense sampling of patches while keeping the stable quad orientation.…”

Recovery of missing samples using sparse approximation via a Convex SIMilarity measure

“…The convexity property of CSIM gives the guarantee to use the Alternating Direction Method of Multipliers (ADMM) [18] to solve (8). Hence, the augmented Lagrangian cost function is:…”

Unsupervised change detection in SAR images using curvelet and L1-norm based soft segmentation

“…It is well known that the closed-form solution of this sub-problem can be expressed using the soft shrinkage (Goldstein and Osher 2009;Li and Zeng 2014), that is,…”