Related papers: An Image Segmentation Model with Transformed Total…
In the last decades, unsupervised deep learning based methods have caught researchers attention, since in many real applications, such as medical imaging, collecting a great amount of training examples is not always feasible. Moreover, the…
We consider a class of integer-constrained optimization problems governed by partial differential equation (PDE) constraints and regularized via total variation (TV) in the context of topology optimization. The presence of discrete design…
In image processing, Total Variation (TV) regularization models are commonly used to recover blurred images. One of the most efficient and popular methods to solve the convex TV problem is the Alternating Direction Method of Multipliers…
The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is…
While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or…
In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…
In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anisotropic extension of the classical isotropic Total Variation (TV) regularizer. The proposed regularizer comes…
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…
Travel-time tomography forces a trade-off between mesh resolution and stability in which the regularizer choice dominates what can be recovered. We introduce MIMIR, a differentiable framework that represents the 2D velocity field as a…
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 objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii)…
Recently, non-convex regularisation models have been introduced in order to provide a better prior for gradient distributions in real images. They are based on using concave energies $\phi$ in the total variation type functional…
In this paper we demonstrate that the framework of nonlinear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more general image manipulation tasks. The well-localized and…
In this paper, we propose a vector total variation (VTV) of feature image model for image restoration. The VTV imposes different smoothing powers on different features (e.g. edges and cartoons) based on choosing various regularization…
Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…
Flash X-ray computed tomography (CT) is an important imaging modality for characterization of high-speed dynamic events, such as Kolsky bar impact experiments for the study of mechanical properties of materials subjected to impulsive…
Total Generalized Variation (TGV) has recently been proven certainly successful in image processing for preserving sharp features as well as smooth transition variations. However, none of the existing works aims at numerically calculating…
In this thesis, we offer a thorough investigation of different regularisation terms used in variational imaging problems, together with detailed optimisation processes of these problems. We begin by studying smooth problems and partially…
In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is…
Over the last 30 years a plethora of variational regularisation models for image reconstruction has been proposed and thoroughly inspected by the applied mathematics community. Among them, the pioneering prototype often taught and learned…