相关论文: Fractional total variation denoising model with $L…

Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize…

We review some recent learning approaches in variational imaging, based on bilevel optimisation, and emphasize the importance of their treatment in function space. The paper covers both analytical and numerical techniques. Analytically, we…

Analysis sparsity is a common prior in inverse problem or machine learning including special cases such as Total Variation regularization, Edge Lasso and Fused Lasso. We study the geometry of the solution set (a polyhedron) of the analysis…

We consider the recovery of a continuous domain piecewise constant image from its non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero levelset of…

The superior performance of Deformable Convolutional Networks arises from its ability to adapt to the geometric variations of objects. Through an examination of its adaptive behavior, we observe that while the spatial support for its neural…

An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element…

Total variation flow, total variation regularization and the taut string algorithm are known to be equivalent filters for one-dimensional discrete signals. In addition, the filtered signal simultaneously minimizes a large number of convex…

In this paper, we focus on learning optimal parameters for PDE-based image regularization and decomposition. First we learn the regularization parameter and the differential operator for gray-scale image denoising using the fractional…

We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian…

Convolutional neural networks (CNNs) have shown outstanding performance on image denoising with the help of large-scale datasets. Earlier methods naively trained a single CNN with many pairs of clean-noisy images. However, the conditional…

Experimentally acquired microscopy images are unavoidably affected by the presence of noise and other unwanted signals, which degrade their quality and might hide relevant features. With the recent increase in image acquisition rate, modern…

This paper deals with the problem of reconstructing a depth map from a sequence of differently focused images, also known as depth from focus or shape from focus. We propose to state the depth from focus problem as a variational problem…

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 consider one-dimensional variants of the classical first order total variation denoising model introduced by Rudin, Osher and Fatemi. This study is based on our previous work on various denoising and inpainting problems in image…

Variational models with coupling terms are becoming increasingly popular in image analysis. They involve auxiliary variables, such that their energy minimisation splits into multiple fractional steps that can be solved easier and more…

We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and…

This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…

We analyse a variational regularisation problem for mixed noise removal that was recently proposed in [14]. The data discrepancy term of the model combines $L^1$ and $L^2$ terms in an infimal convolution fashion and it is appropriate for…

While Total Variation (TV) excels in noise reduction and edge preservation, its reliance on a scalar regularization parameter limits adaptivity. In this study, we present a Learnable Total Variation (LTV) framework coupling an unrolled TV…

The goal of this paper is to present a novel approach for total variation regularization and Sobolev minimization, which are prominent tools for variational imaging. Thereby we use derivative free characterizations of the total variation…