Related papers: Real order (an)-isotropic total variation in image…
In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed in [3] where an automated parameter selection rule for…
We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised…
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…
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…
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…
In this paper we study the one dimensional second order total generalised variation regularisation (TGV) problem with $L^{2}$ data fitting term. We examine some properties of this model and we calculate exact solutions using simple…
We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…
Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an $L^{\tau}$-data fidelity term, $\tau\in \{1,2\}$, are presented. The automated selection of the regularization…
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…
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…
Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image, but they tend to blur the…
We study a general class of infimal convolution type regularisation functionals suitable for applications in image processing. These functionals incorporate a combination of the total variation ($\mathrm{TV}$) seminorm and $\mathrm{L}^{p}$…
We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian…
The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the…
We give a comprehensive survey on a class of higher order variational problems which are motivated by applications in mathematical imaging. The overall aim of this note is to investigate if and in which manner results from the first…
Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations of the imaging…
We introduce a new regularizer in the total variation family that promotes reconstructions with a given Lipschitz constant (which can also vary spatially). We prove regularizing properties of this functional and investigate its connections…
New fractional $r$-order seminorms, $TGV^r$, $r\in \mathbb R$, $r\geq 1$, are proposed in the one-dimensional (1D) setting, as a generalization of the integer order $TGV^k$-seminorms, $k\in\mathbb{N}$. The fractional $r$-order…
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…
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…