相关论文: Total variation regularization for manifold-valued…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
We sketch an application of proximal algorithms to the deformation of de Rham currents into cycles, which is presented as a convex optimization problem. Emphasis is placed on the use of total variation denoising for differential forms,…
In a number of tomographic applications, data cannot be fully acquired, resulting in a severely underdetermined image reconstruction. In such cases, conventional methods lead to reconstructions with significant artifacts. To overcome these…
We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the…
This work considers using reduced basis techniques in connection to (smoothened) total variation regularization in electrical impedance tomography, but analogous ideas can also be used for other inverse elliptic boundary value problems. It…
When generalizing schemes for real-valued data approximation or decomposition to data living in Riemannian manifolds, tangent space-based schemes are very attractive for the simple reason that these spaces are linear. An open challenge is…
In this paper, we propose a variational approach for video denoising, based on a total directional variation (TDV) regulariser proposed in Parisotto et al. (2018), for image denoising and interpolation. In the TDV regulariser, the…
The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel intensities. The TV method has been widely applied in image…
Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total…
This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is…
Total variation denoising (TVD) is a classical method for denoising and curve fitting, yet an explicit pointwise description of its fitted values has only recently been established in the mean regression setting by arXiv:2410.03041v4. This…
This work is about the total variation (TV) minimization which is used for recovering gradient-sparse signals from compressed measurements. Recent studies indicate that TV minimization exhibits a phase transition behavior from failure to…
Capturing complex high-order interactions among data is an important task in many scenarios. A common way to model high-order interactions is to use hypergraphs whose topology can be mathematically represented by tensors. Existing methods…
The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on…
Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…
We propose a new type of regularization functional for images called oscillation total generalized variation (TGV) which can represent structured textures with oscillatory character in a specified direction and scale. The infimal…
The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images, such as sharp edges and enables spectral, scale, and texture analysis.…
We consider $L^1$-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is non-convex for circle-valued data. In this paper,…
The handling of manifold-valued data, for instance, plays a central role in color restoration tasks relying on circle- or sphere-valued color models, in the study of rotational or directional information related to the special orthogonal…
Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an $L^{\tau}$-data fidelity term, $\tau\in \{1,2\}$, are presented. The automated selection of the regularization…