Related papers: Deterministic guarantees for $L^{1}$-reconstructio…

Joint camera pose and dense geometry estimation from a set of images or a monocular video remains a challenging problem due to its computational complexity and inherent visual ambiguities. Most dense incremental reconstruction systems…

In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of $L^p(\Rd), 1\le p\le \infty$, associated with an idempotent integral operator whose kernel has certain off-diagonal decay and regularity.…

Scientific and commercial data is often incomplete. Recovery of the missing information is an important pre-processing step in data analysis. Real-world data can in many cases be represented as a superposition of two or more different types…

We consider a hyperbolic conservation law posed on an (N+1)-dimensional spacetime, whose flux is a field of differential forms of degree N. Generalizing the classical Kuznetsov's method, we derive an L1 error estimate which applies to a…

We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…

In this paper, we present a method for denoising and reconstruction of low-dimensional manifold in high-dimensional space. We suggest a multidimensional extension of the Locally Optimal Projection algorithm which was introduced by Lipman et…

We analyze representative ill-posed scenarios of tomographic PIV with a focus on conditions for unique volume reconstruction. Based on sparse random seedings of a region of interest with small particles, the corresponding systems of linear…

Let $V$ be a set of $n$ points in $\mathbb{R}^d$, and suppose that the distance between each pair of points is revealed independently with probability $p$. We study when this information is sufficient to reconstruct large subsets of $V$, up…

This paper focuses on the problem of 3D human reconstruction from 2D evidence. Although this is an inherently ambiguous problem, the majority of recent works avoid the uncertainty modeling and typically regress a single estimate for a given…

Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…

The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is…

We introduce a new method for the reconstruction of a function from linear measurements by means of oblique projections. The space spanned by the measurement vectors may be different from the subspace in which the function is reconstructed.…

The geometric median, also called $L^{1}$-median, is often used in robust statistics. Moreover, it is more and more usual to deal with large samples taking values in high dimensional spaces. In this context, a fast recursive estimator has…

We establish $L^p$ error estimates for monotone numerical schemes approximating Hamilton-Jacobi equations on the $d$-dimensional torus. Using the adjoint method, we first prove a $L^1$ error bound of order one for finite-difference and…

We develop a novel method to construct uniformly valid confidence bands for a nonparametric component $f_1$ in the sparse additive model $Y=f_1(X_1)+\ldots + f_p(X_p) + \varepsilon$ in a high-dimensional setting. Our method integrates sieve…

Laws of large numbers establish asymptotic guarantees for recovering features of a probability distribution using independent samples. We introduce a framework for proving analogous results for recovery of the $\sigma$-field of a…

Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an…

A posteriori estimates give bounds on the error between the unknown solution of a partial differential equation and its numerical approximation. We present here the methodology based on H1-conforming potential and H(div)-conforming…

We identify sharp spaces and prove quantitative and non-quantitative stability results for the logarithmic Sobolev inequality involving Wasserstein and $L^p$ metrics. The techniques are based on optimal transport theory and Fourier…

The discrete wave equation in a multidimensional uniform space with local defects and sources is considered. The characterization of all possible defect configurations corresponding to given amplitudes of waves at the receivers (detectors)…