相关论文: A note on sampling recovery of multivariate functi…
Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…
Let $\mathbb{T}^d$ denote the $d$-dimensional torus. We consider the problem of optimally recovering a target function $f^*:\mathbb{T}^d\rightarrow \mathbb{C}$ from samples of its Fourier coefficients. We make classical smoothness…
We investigate the approximation of $d$-variate periodic functions in Sobolev spaces of dominating mixed (fractional) smoothness $s>0$ on the $d$-dimensional torus, where the approximation error is measured in the $L_2-$norm. In other…
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…
We provide sufficient conditions on a family of functions $(\phi_\alpha)_{\alpha\in A}:\mathbb{R}^d\to\mathbb{R}$ for sampling of multivariate bandlimited functions at certain nonuniform sequences of points in $\mathbb{R}^d$. We consider…
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…
This paper is a direct followup of the recent author's paper. In this paper we continue to analyze approximation and recovery properties with respect to systems satisfying universal sampling discretization property and a special…
We present improved sampling complexity bounds for stable and robust sparse recovery in compressed sensing. Our unified analysis based on l1 minimization encompasses the case where (i) the measurements are block-structured samples in order…
We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas…
We investigate the rate of convergence of linear sampling numbers of the embedding $H^{\alpha,\beta} (\mathbb{T}^d) \hookrightarrow H^\gamma (\mathbb{T}^d)$. Here $\alpha$ governs the mixed smoothness and $\beta$ the isotropic smoothness in…
By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…
In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that…
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…
We consider the problem of optimal recovery of an element $u$ of a Hilbert space $\mathcal{H}$ from $m$ measurements obtained through known linear functionals on $\mathcal{H}$. Problems of this type are well studied \cite{MRW} under an…
We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic…
We study optimal algorithms in adaptive sampling recovery of smooth functions defined on the unit $d$-cube ${\II}^d:= [0,1]^d$. The recovery error is measured in the quasi-norm $\|\cdot\|_q$ of $L_q := L_q(\II^d)$. For $B$ a subset in…
This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform…
Using Coherent-State (CS) techniques, we prove a sampling theorem for holomorphic functions on the hyperboloid (or its stereographic projection onto the open unit disk $\mathbb D_1$), seen as a homogeneous space of the pseudo-unitary group…
This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…
We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery process is calculated with respect to different Orlicz norms.…