Related papers: Closed-Form Approximation of the Total Variation P…
We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…
In this paper we analyse an infimal convolution type regularisation functional called $\mathrm{TVL}^{\infty}$, based on the total variation ($\mathrm{TV}$) and the $\mathrm{L}^{\infty}$ norm of the gradient. The functional belongs to a more…
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…
Owing to its significant success, the prior imposed on gradient maps has consistently been a subject of great interest in the field of image processing. Total variation (TV), one of the most representative regularizers, is known for its…
The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numerical solution of convex optimization problems,…
Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…
Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal…
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 work considers the use of Total variation (TV) minimization in the recovery of a given gradient sparse vector from Gaussian linear measurements. It has been shown in recent studies that there exist a sharp phase transition behavior in…
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…
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…
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 consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an…
In this article, two closed and convex sets for blind deconvolution problem are proposed. Most blurring functions in microscopy are symmetric with respect to the origin. Therefore, they do not modify the phase of the Fourier transform (FT)…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is…
Compressed sensing (CS) methods in magnetic resonance imaging (MRI) offer rapid acquisition and improved image quality but require iterative reconstruction schemes with regularization to enforce sparsity. Regardless of the difficulty in…
This paper is concerned with an elliptic optimal control problem with total variation (TV) restriction on the control in the constraints. We introduce a regularized optimal control problem by applying a quadratic regularization of the dual…
We present an analysis of total-variation (TV) on non-Euclidean parameterized surfaces, a natural representation of the shapes used in 3D graphics. Our work explains recent experimental findings in shape spectral TV [Fumero et al., 2020]…
Solving an optimization problem whose objective function is the sum of two convex functions has received considerable interests in the context of image processing recently. In particular, we are interested in the scenario when a…