相关论文: Total Generalized Variation Regularization in Vari…
Many methods for processing scalar and vector valued images, volumes and other data in the context of inverse problems are based on variational formulations. Such formulations require appropriate regularization functionals that model…
Total Variation (TV) based regularization has been widely applied in restoration problems due to its simple derivative filters based formulation and robust performance. While first order TV suffers from staircase effect, second order TV…
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…
Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…
The concept of generalized cross-validation (GCV) is applied to modified total generalized variation (MTGV) regularization. Current implementations of the MTGV regularization rely on manual (or semi-manual) hyperparameter optimization,…
Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…
In this paper, we propose the Graph-Fused Multivariate Regression (GFMR) via Total Variation regularization, a novel method for estimating the association between a one-dimensional or multidimensional array outcome and scalar predictors.…
Total variation(TV) regularization is applied to X-Ray computed tomography(CT) in an effort to reduce metal artifacts. Tikhonov regularization with $L^2$ data fidelity term and total variation regularization is augmented in this novel model…
We introduce a first order Total Variation type regulariser that decomposes a function into a part with a given Lipschitz constant (which is also allowed to vary spatially) and a jump part. The kernel of this regulariser contains all…
The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in the modelling of physical phenomena such as traffic flow. In this paper, we propose a novel…
Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…
We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an…
In this paper, we consider a backward problem for a time-space fractional diffusion process. For this problem, we propose to construct the initial data by minimizing data residual error in fourier space domain and variable total variation…
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…
A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…
This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary…
To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order…
In this paper, we propose image restoration models using optimal transport (OT) and total variation regularization. We present theoretical results of the proposed models based on the relations between the dual Lipschitz norm from OT and the…
There is currently a great deal of interest in the 4D-Var data assimilation scheme, in which one uses observational data to find the optimal initial condition for a differential equation by minimizing a cost function over the set of all…
The conjugate gradient (CG) method is commonly used for the rapid solution of least squares problems. In image reconstruction, the problem can be ill-posed and also contaminated by noise; due to this, approaches such as regularization…