Some imaging inverse problems may require the solution to simultaneously exhibit properties that are not enforceable by a single regularizer. One way to attain this goal is to use a linear combinations of regularizers, thus encouraging the solution to simultaneously exhibit the characteristics enforced by each individual regularizer. In this paper, we address the optimization problem resulting ...

Several ways to generalize scalar total variation to vector-valued functions have been proposed in the past. In this paper, we give a detailed analysis of a variant we denote by TVJ , which has not been previously explored as a regularizer. The contributions of the manuscript are twofold: on the theoretical side, we show that TVJ can be derived from the generalized Jacobians from geometric meas...

The aim of image restoration is to obtain a higher quality desired image from a degraded image. In this strategy, an image inpainting method fills the degraded or lost area of the image by appropriate information. This is performed in such a way so that the obtained image is undistinguishable for a casual person who is unfamiliar with the original image. In this paper, different images are degr...

We introduce a generic convex energy functional that is suitable for both grayscale and vector-valued images. Our functional is based on the eigenvalues of the structure tensor, therefore it penalizes image variation at every point by taking into account the information from its neighborhood. It generalizes several existing variational penalties, such as the Total Variation and vectorial extens...

We consider additive models built with trend filtering, i.e., additive models whose components are each regularized by the (discrete) total variation of their (k+1)st (discrete) derivative, for a chosen integer k ≥ 0. This results in kth degree piecewise polynomial components, (e.g., k = 0 gives piecewise constant components, k = 1 gives piecewise linear, k = 2 gives piecewise quadratic, etc.)....

Multiplicative noise removal is a quite challenging problem in image denoising. In recent years, hyper-Laplacian prior information has been successfully introduced the denoising and significant effects have achieved. this paper, we propose new hybrid regularizer model for removing multiplicative noise. The proposed consists of non-convex higher-order total variation overlapping group sparsity o...

We introduce a novel second-order regularizer, the Affine Total-Variation term, to capture the geometry of piecewise affine functions. The approach is characterized by two convex decompositions of a given image into piecewise affine structure and texture and noise, respectively. A convergent multiplier-based method is presented for computing a global optimum by computationally cheap iterative s...

A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. semi-supervised (bilevel) training scheme, which provides a simultaneous optimization with respect to parameters and new regularizers, studied. Also, finite approximation method, used solve global solutions such introduced analyzed.

In this article, we propose a total generalized variation (TGV) [1] based model for removing multiplicative Gamma noise. To preserve edge more, we adopt a nonconvex regularizer to TGV regularization term. The model integrates the data-fitting energy proposed in [2] with a spatially adaptive regularization parameter (SARP) approach. The data-fidelity term enables to deal with heavy multiplicativ...

Motion cues are an integral part of our visual experience, and therefore it is not surprising that the recovery of motion information from image sequences is a prominent problem in computer vision. Such motion estimates can, e.g., be obtained using nonparametric variational techniques, but while these techniques yield accurate results on a diverse range of image sequences, there are still a num...