Related papers: TV homogenization inequalities
We define the space of functions of bounded variation ($BV$) on the graph. Using the notion of divergence of flows on graphs, we show that the unit ball of the dual space to $BV$ in the graph setting can be described as the image of the…
If one seeks to estimate the total variation between two product measures $||P^\otimes_{1:n}-Q^\otimes_{1:n}||$ in terms of their marginal TV sequence $\delta=(||P_1-Q_1||,||P_2-Q_2||,\ldots,||P_n-Q_n||)$, then trivial upper and lower…
We consider inhomogeneous Bernoulli measures of the form $\prod_{x\in\Lambda} p_x$ where $p_x$ are prescribed and uniformly bounded above and below away from 0 and 1. A comparison inequality is proved between the Kawasaki and…
In this paper we present a novel iterative procedure for multichannel image and data reconstruction using Bregman distances. With the motivation that multiple channels sharing a common subgradient with respect to a suitable regularization…
The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…
We study the behaviour of Tikhonov regularisation on topological spaces with multiple regularisation terms. The main result of the paper shows that multi-parameter regularisation is well-posed in the sense that the results depend…
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…
This paper studies convergence of empirical measures smoothed by a Gaussian kernel. Specifically, consider approximating $P\ast\mathcal{N}_\sigma$, for $\mathcal{N}_\sigma\triangleq\mathcal{N}(0,\sigma^2 \mathrm{I}_d)$, by…
We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are…
Consider a discrete time Markov chain with rather general state space which has an invariant probability measure $\mu$. There are several sufficient conditions in the literature which guarantee convergence of all or $\mu$-almost all…
Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…
Labelled Markov chains (LMCs) are widely used in probabilistic verification, speech recognition, computational biology, and many other fields. Checking two LMCs for equivalence is a classical problem subject to extensive studies, while the…
One of the fundamental assumptions of compressive sensing (CS) is that a signal can be reconstructed from a small number of samples by solving an optimization problem with the appropriate regularization term. Two standard regularization…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
We consider the problem of recovering the superposition of $R$ distinct complex exponential functions from compressed non-uniform time-domain samples. Total Variation (TV) minimization or atomic norm minimization was proposed in the…
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…
This work is about the total variation (TV) minimization which is used for recovering gradient-sparse signals from compressed measurements. Recent studies indicate that TV minimization exhibits a phase transition behavior from failure to…
By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell's equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic…
In this paper, we establish a novel connection between total variation (TV) distance estimation and probabilistic inference. In particular, we present an efficient, structure-preserving reduction from relative approximation of TV distance…
In this paper, we consider using total variation minimization to recover signals whose gradients have a sparse support, from a small number of measurements. We establish the proof for the performance guarantee of total variation (TV)…