Related papers: Approximation Theory of Total Variation Minimizati…
Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an…
In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…
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…
This paper introduces a novel approach for epidemic nowcasting and forecasting over networks using total variation (TV) denoising, a method inspired by classical signal processing techniques. Considering a network that models a population…
Two-sample testing, where we aim to determine whether two distributions are equal or not equal based on samples from each one, is challenging if we cannot place assumptions on the properties of the two distributions. In particular,…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically…
Spin systems form an important class of undirected graphical models. For two Gibbs distributions $\mu$ and $\nu$ induced by two spin systems on the same graph $G = (V, E)$, we study the problem of approximating the total variation distance…
In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error…
The no-broadcasting theorem, a fundamental limitation on the communication of quantum information, holds that a physical process cannot broadcast copies of an unknown quantum state to two or more receivers. Recent work has explored ways of…
We propose a new superresolution imaging technique for interferometry using sparse modeling, utilizing two regularization terms: the $\ell_1$-norm and a new function named Total Squared Variation (TSV) of the brightness distribution. TSV is…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Weighted $\ell_1$-minimization has been studied as a technique for the reconstruction of a sparse signal from compressively sampled measurements when prior information about the signal, in the form of a support estimate, is available. In…
Previous work showed that total variation superiorization (TVS) improves reconstructed image quality in proton computed tomography (pCT). The structure of the TVS algorithm has evolved since then and this work investigated if this new…
In this paper, we propose a general approach for explicit a posteriori error representation for convex minimization problems using basic convex duality relations. Exploiting discrete orthogonality relations in the space of element-wise…
We consider a patch-based learning approach defined in terms of neural networks to estimate spatially adaptive regularisation parameter maps for image denoising with weighted Total Variation (TV) and test it to situations when the noise…
Models of discrete-valued outcomes are easily misspecified if the data exhibit zero-inflation, overdispersion or contamination. Without additional knowledge about the existence and nature of this misspecification, model inference and…
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…
Single-image super-resolution is the process of increasing the resolution of an image, obtaining a high-resolution (HR) image from a low-resolution (LR) one. By leveraging large training datasets, convolutional neural networks (CNNs)…
In this paper, we devise a $\operatorname{prox}$-based semi-smooth Newton method for the non-differentiable TV-minimization problem. To this end, the primal-dual optimality conditions are reformulated as a nonlinear operator equation with…