Related papers: Real order (an)-isotropic total variation in image…
We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian…
Recently variational models with priors involving first and second order derivatives resp. differences were successfully applied for image restoration. There are several ways to incorporate the derivatives of first and second order into the…
Magnetic Particle Imaging (MPI) is a recent imaging modality where superparamagnetic nanoparticles are employed as tracers. The reconstruction task is to obtain the spatial particle distribution from a voltage signal induced by the…
This work proposes the variable exponent Lebesgue modular as a replacement for the 1-norm in total variation (TV) regularization. It allows the exponent to vary with spatial location and thus enables users to locally select whether to…
A fundamental concept in solving inverse problems is the use of regularizers, which yield more physical and less-oscillatory solutions. Total variation (TV) has been widely used as an edge-preserving regularizer. However, objects are often…
Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our…
We propose a method for fast and automatic estimation of spatially dependent regularization maps for total variation-based (TV) tomography reconstruction. The estimation is based on two distinct sub-networks, with the first sub-network…
The cross-channel deblurring problem in color image processing is difficult to solve due to the complex coupling and structural blurring of color pixels. Until now, there are few efficient algorithms that can reduce color artifacts in…
The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In this paper, in order to alleviate the staircase effect,…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…
This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential feature is to encode the image via a sparse vector field,…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…
In a class of piecewise-constant image segmentation models, we propose to incorporate a weighted difference of anisotropic and isotropic total variation (AITV) to regularize the partition boundaries in an image. In particular, we replace…
A Bayesian hierarchical model for total variation regularisation is presented in this paper. All the parameters of an inverse problem, including the "regularisation parameter", are estimated simultaneously from the data in the model. The…
We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a…
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…
Primal-dual splitting involving proximity operators in order to be able to find some approximation to the minimizer for a general form of Tikhonov type functional is in the focus of this work. This approximation is produced by a pair of…