相关论文: L1TV computes the flat norm for boundaries

Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…

Distance geometry problem belongs to a class of hard problems in classical computation that can be understood in terms of a set of inputs processed according to a given transformation, and for which the number of possible outcomes grows…

Area openings and closings are morphological filters which efficiently suppress impulse noise from an image, by removing small connected components of level sets. The problem of an objective choice of threshold for the area remains open.…

We propose a new method with $\mathcal{L}_2$ distance that maps one $N$-dimensional distribution to another, taking into account available information about correspondences. We solve the high-dimensional problem in 1D space using an…

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…

As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…

Lattice decoders constructed with neural networks are presented. Firstly, we show how the fundamental parallelotope is used as a compact set for the approximation by a neural lattice decoder. Secondly, we introduce the notion of…

We present a progressive image decomposition method based on a novel non-linear filter named Sub-window Variance filter. Our method is specifically designed for image detail enhancement purpose; this application requires extraction of image…

This paper is devoted to dimensional reductions via the norm resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The efficiency of our abstract tool is demonstrated by its…

The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…

Consider observing an undirected network that is `noisy' in the sense that there are Type I and Type II errors in the observation of edges. Such errors can arise, for example, in the context of inferring gene regulatory networks in genomics…

A new thresholding strategy for the estimation of a deterministic image immersed in noise is introduced. The threshold is combined with a wavelet decomposition, where the wavelet coefficient of the image at any fixed value of the…

This paper addresses the study and applications of polyhedral duality of locally convex topological vector (LCTV) spaces. We first revisit the classical Rockafellar's proper separation theorem for two convex sets one which is polyhedral and…

As deep learning (DL) is being rapidly pushed to edge computing, researchers invented various ways to make inference computation more efficient on mobile/IoT devices, such as network pruning, parameter compression, and etc. Quantization, as…

Singular spectrum analysis is developed as a nonparametric spectral decomposition of a time series. It can be easily extended to the decomposition of multidimensional lattice-like data through the filtering interpretation. In this…

In this article, we study new methods for constructing uninorms on bounded lattices. First, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are…

Most of the existing methods for sparse signal recovery assume a static system: the unknown signal is a finite-length vector for which a fixed set of linear measurements and a sparse representation basis are available and an L1-norm…

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…

A new measure to assess the centrality of vertices in an undirected and connected graph is proposed. The proposed measure, L1 centrality, can adequately handle graphs with weights assigned to vertices and edges. The study provides tools for…