Related papers: Total variation regularization with variable Lebes…
We propose a second-order total generalized variation (TGV) regularization for the reconstruction of the initial condition in variational data assimilation problems. After showing the equivalence between TGV regularization and the Bayesian…
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…
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…
Total variation regularization has proven to be a valuable tool in the context of optimal control of differential equations. This is particularly attributed to the observation that TV-penalties often favor piecewise constant minimizers with…
A computational method is introduced for choosing the regularization parameter for total variation (TV) regularization. The approach is based on computing reconstructions at a few different resolutions and various values of regularization…
We address the image restoration problem under Poisson noise corruption. The Kullback-Leibler divergence, which is typically adopted in the variational framework as data fidelity term in this case, is coupled with the second-order Total…
Over the last decade or so, reconstruction methods using $\ell_1$ regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The…
The total generalized variation (TGV) is a popular regularizer in inverse problems and imaging combining discontinuous solutions and higher order smoothing. In particular, empirical observations suggest that its order two version strongly…
The core of many approaches for the resolution of variational inverse problems arising in signal and image processing consists of promoting the sought solution to have a sparse representation in a well-suited space. A crucial task in this…
Total variation (TV) regularization is a classical tool for image denoising, but its convex $\ell_1$ formulation often leads to staircase artifacts and loss of contrast. To address these issues, we introduce the Transformed $\ell_1$ (TL1)…
This paper considers the constrained total variation (TV) denoising problem for complex-valued images. We extend the definition of TV seminorms for real-valued images to dealing with complex-valued ones. In particular, we introduce two…
Direction-guided structure tensor total variation (DSTV) is a recently proposed regularization term that aims at increasing the sensitivity of the structure tensor total variation (STV) to the changes towards a predetermined direction.…
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 paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation. To deal with the ill-posedness of the problem, we transform the problem into an optimal control problem with total variational…
In this paper, we propose Total Variation Regularized Tensor-on-scalar Regression(TVTR), a novel method for estimating the association between a tensor outcome (a one dimensional or multidimensional array) and scalar predictors. While the…
One of the fundamental assumptions of compressive sensing (CS) is that a signal can be reconstructed from a small number of samples by solving an optimization problem with the appropriate regularization term. Two standard regularization…
Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth. Our setup covers earlier variable exponent and double…
In this paper, a variational, multi-dimensional model for image reconstruction is proposed, in which the regularization term consists of the $r$-order (an)-isotropic total variation seminorms $TV^r$, with $r\in \mathbb R^+$, defined via the…
We study a nonlocal version of the total variation-based model with $L^1-$fidelity for image denoising, where the regularizing term is replaced with the fractional $s$-total variation. We discuss regularity of the level sets and uniqueness…
We study decompositions of Nakano type varying exponent Lebesgue norms and spaces. These function spaces are represented here in a natural way as tractable varying $\ell^p$ sums of projection bands. The main results involve embedding the…