相关论文: Functions in Sampling Spaces
We consider the problem of random sampling for band-limited functions. When can a band-limited function $f$ be recovered from randomly chosen samples $f(x_j), j\in \mathbb{N}$? We estimate the probability that a sampling inequality of the…
We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the plane. We identify a large class of lattices, or more generally…
In a previous paper, the author constructed frames and oversampling formulas for band-limited functions, in the framework of the theory of shift-invariant spaces. In this article we study the problem of recovering missing samples. We find a…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a…
The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces of Hilbert-Schmidt operators, finitely generated, with respect to a lattice $\Lambda$ in…
Sampling theory is a discipline in communications engineering involved with the exact reconstruction of continuous signals from discrete sets of sample points. From a physics perspective, this is interesting in relation to the question of…
Successive differences on a sequence of data help to discover some smoothness features of this data. This was one of the main reasons for rewriting the classical interpolation formula in terms of such data differences. The aim of this paper…
We study the random sampling of band-limited functions of several variables. If a bandlimited function with bandwidth one has its essential support on a cube of volume $R^d$, then $\cO (R^d \log R^d)$ random samples suffice to approximate…
The use of unitary invariant subspaces of a Hilbert space $\mathcal{H}$ is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of $L^2(\mathbb{R})$ and also periodic extensions of finite…
Assume that samples of a filtered version of a function in a shift-invariant space are avalaible. This work deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support.…
It is shown that a band limited function on a non-compact symmetric space can be reconstructed in a stable way from some countable sets of values of its convolution with certain distributions of compact support. A reconstruction method in…
Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields. In this survey we present several extensions of the Shannon…
A regular generalized sampling theory in some structured T-invariant subspaces of a Hilbert space H, where T denotes a bounded invertible operator in H, is established in this paper. This is done by walking through the most important cases…
We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of the natural interpolating and sampling sequences for this space. We also find a description of the trace of such…
Spatial sampling is traditionally studied in a static setting where static sensors scattered around space take measurements of the spatial field at their locations. In this paper we study the emerging paradigm of sampling and reconstructing…
The study of sampling signals on graphs, with the goal of building an analog of sampling for standard signals in the time and spatial domains, has attracted considerable attention recently. Beyond adding to the growing theory on graph…
The sampling of functions of bounded variation (BV) is a long-standing problem in op- timization. The ability to sample such functions has relevance in the field of variational inverse problems, where the standard theory fails to guarantee…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
Mobile sensing has been recently proposed for sampling spatial fields, where mobile sensors record the field along various paths for reconstruction. Classical and contemporary sampling typically assumes that the sampling locations are…