Related papers: A homogenization principle for total variation
The Wasserstein distance provides a notion of dissimilarities between probability measures, which has recent applications in learning of structured data with varying size such as images and text documents. In this work, we study the…
General sufficient conditions are given for absolute continuity and convergence in variation of the distributions of the unctionals on a probability space, generated by a Poisson point measure. The phase space of the Poisson point measure…
Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for…
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these…
We are interested in the estimation of the distance in total variation $$ \Delta := \|P_{f(X)} - P_{g(X)}\|_{\mathrm var} $$ between distributions of random variables $f(X)$ and $g(X)$ in terms of proximity of $f$ and $g.$ We propose a…
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 propose a second-order total generalized variation (TGV) regularization for the reconstruction of the initial condition in variational data assimilation problems. After showing the equivalence between TGV regularization and the Bayesian…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
Let $(T,d)$ be a metric space and $\phi:\mathbb{R}_+\to \mathbb{R}$ an increasing, convex function with $\phi(0)=0$. We prove that if $m$ is a probability measure $m$ on $T$ which is majorizing with respect to $d,\phi$, that is,…
We introduce distance measures between quantum states, measurements, and channels based on their statistical distinguishability in generic experiments. Specifically, we analyze the average Total Variation Distance (TVD) between output…
Quantum coherence, as a direct manifestation of the quantum superposition principle, is a crucial resource in quantum information processing. Block coherence resource theory generalizes the traditional coherence framework by defining…
This work aims to explore the regularity properties of the smoothed-TV regularization for the functions is of the class H\"older continuous. Over some compact and convex domain $\Omega,$ we study construction of multivariate function…
Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…
The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical…
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…
We propose a novel approach to quantify quantum coherence which, contrary to the previous ones, does not rely on resource theory but rather on ontological considerations. In this framework, coherence is understood as the ability for a…
A combinatorial proof of the Gaussian product inequality (GPI) is given under the assumption that each component of a centered Gaussian random vector $\boldsymbol{X} = (X_1, \ldots, X_d)$ of arbitrary length can be written as a linear…
We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible…
We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…
We study the JKO scheme for the total variation, characterize the optimizers, prove some of their qualitative properties (in particular a form of maximum principle and in some cases, a minimum principle as well). Finally, we establish a…