Related papers: Compact Representation of n-th order TGV
Based on transformed $\ell_1$ regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its performance, we…
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,…
An optimization framework is presented for minimizing the energy functional developed around a generalized equation governing physical systems such as fluid dynamics, particle transport, phase transition, and other related systems. The…
With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…
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…
Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray…
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)…
We introduce a novel regulariser based on the natural vector field operations gradient, divergence, curl and shear. For suitable choices of the weighting parameters contained in our model it generalises well-known first- and second-order…
This article is the second work in our series of papers dedicated to image processing models based on the fractional order total variation $TV^r$. In our first work of this series, we studied key analytic properties of these semi-norms.…
We explore the use of the recently proposed "total nuclear variation" (TNV) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued…
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…
This work combines three paradigms of image processing: i) the total variation approach to denoising, ii) the superior structure of hexagonal lattices, and iii) fast and exact graph cut optimization techniques. Although isotropic in theory,…
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…
In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold-valued data with indirect measurement operators. We provide…
We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…
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…
Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved…
A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…
Multi-energy CT based on compression sensing theory with sparse-view sampling can effectively reduce radiation dose and maintain the quality of the reconstructed image. However,when the projection data are noisy, the reconstructed image can…
In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…