相关论文: Learning to solve TV regularized problems with unr…
Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well…
The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide…
The space-discrete Total Variation (TV) flow is analyzed using several mode decomposition techniques. In the one-dimensional case, we provide analytic formulations to Dynamic Mode Decomposition (DMD) and to Koopman Mode Decomposition (KMD)…
Over the last decades, the total variation (TV) evolved to one of the most broadly-used regularisation functionals for inverse problems, in particular for imaging applications. When first introduced as a regulariser, higher-order…
This paper proposes to solve the Total Variation regularized models by finding the residual between the input and the unknown optimal solution. After analyzing a previous method, we developed a new iterative algorithm, named as Residual…
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…
We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there…
Popular methods for finding regularized solutions to inverse problems include sparsity promoting $\ell_1$ regularization techniques, one in particular which is the well known total variation (TV) regularization. More recently, several…
Total variation (TV) denoising is a nonparametric smoothing method that has good properties for preserving sharp edges and contours in objects with spatial structures like natural images. The estimate is sparse in the sense that TV…
Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in…
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…
We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These…
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…
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,…
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…
Total generalization variation (TGV) is a very powerful and important regularization for various inverse problems and computer vision tasks. In this paper, we proposed a semismooth Newton based augmented Lagrangian method to solve this…
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…
High radiation dose in CT scans increases a lifetime risk of cancer and has become a major clinical concern. Recently, iterative reconstruction algorithms with Total Variation (TV) regularization have been developed to reconstruct CT images…
Neural network approaches have been demonstrated to work quite well to solve partial differential equations in practice. In this context approaches like physics-informed neural networks and the Deep Ritz method have become popular. In this…