Related papers: Dynamical sampling
We consider bounded operators $A$ acting iteratively on a finite set of vectors $\{f_i : i\in I\}$ in a Hilbert space $\mathcal H$ and address the problem of providing necessary and sufficient conditions for the collection of iterates…
We review some of the recent developments and prove new results concerning frames and Bessel systems generated by iterations of the form $\{A^ng: g\in G,\, n=0,1,2,\dots \}$, where $A$ is a bounded linear operators on a separable complex…
In this paper, we investigate frames for $L_2[-\pi,\pi]^d$ consisting of exponential functions in connection to oversampling and nonuniform sampling of bandlimited functions. We derive a multidimensional nonuniform oversampling formula for…
We consider the problem of spatiotemporal sampling in which an initial state $f$ of an evolution process $f_t=A_tf$ is to be recovered from a combined set of coarse samples from varying time levels $\{t_1,\dots,t_N\}$. This new way of…
Dynamical sampling deals with representations of a frame $\{ f_k \}_{k=1}^\infty$ as an orbit $\{ T^n \varphi \}_{n=0}^\infty$ of a linear and possibly bounded operator $T$ acting on the underlying Hilbert space. It is known that the desire…
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…
In this note, we solve the dynamical sampling problem for a class of shift-preserving operators $L:V\to V$ acting on a finitely generated shift-invariant space $V$. We find conditions on $L$ and a finite set of functions of $V$ so that the…
In this paper we study the continuous dynamical sampling problem at infinite time in a complex Hilbert space $\mathcal{H}$. We find necessary and sufficient conditions on a bounded linear operator $A\in\mathcal{B}(\mathcal{H})$ and a set of…
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…
Dynamical Sampling of frames and tensor products are important topics in harmonic analysis. This paper combines the concepts of dynamical sampling of frames and the Carleson condition in the tensor product of Hardy spaces. Initially we…
The dynamical sampling problem is centered around reconstructing signals that evolve over time according to a dynamical process, from spatial-temporal samples that may be noisy. This topic has been thoroughly explored for one-dimensional…
Motivated by the dynamical sampling problem, we study frames in an infinite dimensional Hilbert space generated by the iterates of a bounded operator T, also known as dynamical frames. We first characterize the operators that generate…
A method to solve the problem f(x) = 0 efficiently on any n-dimensional domain Omega under very broad hypoteses is proposed. The position of the root of f, assumed unique, is found by computing the center of mass of an Omega-shaped object…
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.…
We prove a sampling theorem for infinite-dimensional Paley-Wiener spaces on graphs which allows for stable frame reconstruction. We prove that all sampling sets for a fixed Paley-Wiener space are complements of lambda-sets (i.e. sets where…
In this work, we explore the dynamical sampling problem on $\ell^2(\mathbb{Z})$ driven by a convolution operator defined by a convolution kernel. This problem is inspired by the need to recover a bandlimited heat diffusion field from…
In this note we study the problem of sampling and reconstructing signals which are assumed to lie on or close to one of several subspaces of a Hilbert space. Importantly, we here consider a very general setting in which we allow infinitely…
In this paper we present new constructive methods, random and deterministic, for the efficient subsampling of finite frames in $\mathbb C^m$. Based on a suitable random subsampling strategy, we are able to extract from any given frame with…
Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…
It is a challenge to manage infinite- or high-dimensional data in situations where storage, transmission, or computation resources are constrained. In the simplest scenario when the data consists of a noisy infinite-dimensional signal, we…